On higher dimensional complex Plateau problem
Abstract Let X be a compact connected strongly pseudoconvex CR manifold of real dimension %$2n-1%$ in %${\mathbb {C}}^{N}%$. It has been an interesting question to find an intrinsic smoothness criteria for the complex Plateau problem. For %$n\ge 3%$ and %$N=n+1%$, Yau found a necessary and sufficien...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Du, Rong [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Mathematische Zeitschrift - Berlin : Springer, 1918, 282(2015), 1-2 vom: 26. Okt., Seite 389-403 |
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| Übergeordnetes Werk: |
volume:282 ; year:2015 ; number:1-2 ; day:26 ; month:10 ; pages:389-403 |
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| DOI / URN: |
10.1007/s00209-015-1544-2 |
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| Katalog-ID: |
SPR001928066 |
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| 245 | 1 | 0 | |a On higher dimensional complex Plateau problem |
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| 520 | |a Abstract Let X be a compact connected strongly pseudoconvex CR manifold of real dimension %$2n-1%$ in %${\mathbb {C}}^{N}%$. It has been an interesting question to find an intrinsic smoothness criteria for the complex Plateau problem. For %$n\ge 3%$ and %$N=n+1%$, Yau found a necessary and sufficient condition for the interior regularity of the Harvey–Lawson solution to the complex Plateau problem by means of Kohn–Rossi cohomology groups on X in 1981. For %$n=2%$ and %$N\ge n+1%$, the first and third authors introduced a new CR invariant %$g^{(1,1)}(X)%$ of X. The vanishing of this invariant will give the interior regularity of the Harvey–Lawson solution up to normalization. For %$n\ge 3%$ and %$N>n+1%$, the problem still remains open. In this paper, we generalize the invariant %$g^{(1,1)}(X)%$ to higher dimension as %$g^{(\Lambda ^n 1)}(X)%$ and show that if %$g^{(\Lambda ^n 1)}(X)=0%$, then the interior has at most finite number of rational singularities. In particular, if X is Calabi–Yau of real dimension 5, then the vanishing of this invariant is equivalent to give the interior regularity up to normalization. | ||
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| 700 | 1 | |a Gao, Yun |4 aut | |
| 700 | 1 | |a Yau, Stephen |4 aut | |
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10.1007/s00209-015-1544-2 doi (DE-627)SPR001928066 (SPR)s00209-015-1544-2-e DE-627 ger DE-627 rakwb eng Du, Rong verfasserin aut On higher dimensional complex Plateau problem 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract Let X be a compact connected strongly pseudoconvex CR manifold of real dimension %$2n-1%$ in %${\mathbb {C}}^{N}%$. It has been an interesting question to find an intrinsic smoothness criteria for the complex Plateau problem. For %$n\ge 3%$ and %$N=n+1%$, Yau found a necessary and sufficient condition for the interior regularity of the Harvey–Lawson solution to the complex Plateau problem by means of Kohn–Rossi cohomology groups on X in 1981. For %$n=2%$ and %$N\ge n+1%$, the first and third authors introduced a new CR invariant %$g^{(1,1)}(X)%$ of X. The vanishing of this invariant will give the interior regularity of the Harvey–Lawson solution up to normalization. For %$n\ge 3%$ and %$N>n+1%$, the problem still remains open. In this paper, we generalize the invariant %$g^{(1,1)}(X)%$ to higher dimension as %$g^{(\Lambda ^n 1)}(X)%$ and show that if %$g^{(\Lambda ^n 1)}(X)=0%$, then the interior has at most finite number of rational singularities. In particular, if X is Calabi–Yau of real dimension 5, then the vanishing of this invariant is equivalent to give the interior regularity up to normalization. Cohomology Group (dpeaa)DE-He213 Real Dimension (dpeaa)DE-He213 Pseudoconvex Domain (dpeaa)DE-He213 Holomorphic Vector Bundle (dpeaa)DE-He213 Coherent Sheaf (dpeaa)DE-He213 Gao, Yun aut Yau, Stephen aut Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 282(2015), 1-2 vom: 26. Okt., Seite 389-403 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:282 year:2015 number:1-2 day:26 month:10 pages:389-403 https://dx.doi.org/10.1007/s00209-015-1544-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 282 2015 1-2 26 10 389-403 |
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10.1007/s00209-015-1544-2 doi (DE-627)SPR001928066 (SPR)s00209-015-1544-2-e DE-627 ger DE-627 rakwb eng Du, Rong verfasserin aut On higher dimensional complex Plateau problem 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract Let X be a compact connected strongly pseudoconvex CR manifold of real dimension %$2n-1%$ in %${\mathbb {C}}^{N}%$. It has been an interesting question to find an intrinsic smoothness criteria for the complex Plateau problem. For %$n\ge 3%$ and %$N=n+1%$, Yau found a necessary and sufficient condition for the interior regularity of the Harvey–Lawson solution to the complex Plateau problem by means of Kohn–Rossi cohomology groups on X in 1981. For %$n=2%$ and %$N\ge n+1%$, the first and third authors introduced a new CR invariant %$g^{(1,1)}(X)%$ of X. The vanishing of this invariant will give the interior regularity of the Harvey–Lawson solution up to normalization. For %$n\ge 3%$ and %$N>n+1%$, the problem still remains open. In this paper, we generalize the invariant %$g^{(1,1)}(X)%$ to higher dimension as %$g^{(\Lambda ^n 1)}(X)%$ and show that if %$g^{(\Lambda ^n 1)}(X)=0%$, then the interior has at most finite number of rational singularities. In particular, if X is Calabi–Yau of real dimension 5, then the vanishing of this invariant is equivalent to give the interior regularity up to normalization. Cohomology Group (dpeaa)DE-He213 Real Dimension (dpeaa)DE-He213 Pseudoconvex Domain (dpeaa)DE-He213 Holomorphic Vector Bundle (dpeaa)DE-He213 Coherent Sheaf (dpeaa)DE-He213 Gao, Yun aut Yau, Stephen aut Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 282(2015), 1-2 vom: 26. Okt., Seite 389-403 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:282 year:2015 number:1-2 day:26 month:10 pages:389-403 https://dx.doi.org/10.1007/s00209-015-1544-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 282 2015 1-2 26 10 389-403 |
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10.1007/s00209-015-1544-2 doi (DE-627)SPR001928066 (SPR)s00209-015-1544-2-e DE-627 ger DE-627 rakwb eng Du, Rong verfasserin aut On higher dimensional complex Plateau problem 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract Let X be a compact connected strongly pseudoconvex CR manifold of real dimension %$2n-1%$ in %${\mathbb {C}}^{N}%$. It has been an interesting question to find an intrinsic smoothness criteria for the complex Plateau problem. For %$n\ge 3%$ and %$N=n+1%$, Yau found a necessary and sufficient condition for the interior regularity of the Harvey–Lawson solution to the complex Plateau problem by means of Kohn–Rossi cohomology groups on X in 1981. For %$n=2%$ and %$N\ge n+1%$, the first and third authors introduced a new CR invariant %$g^{(1,1)}(X)%$ of X. The vanishing of this invariant will give the interior regularity of the Harvey–Lawson solution up to normalization. For %$n\ge 3%$ and %$N>n+1%$, the problem still remains open. In this paper, we generalize the invariant %$g^{(1,1)}(X)%$ to higher dimension as %$g^{(\Lambda ^n 1)}(X)%$ and show that if %$g^{(\Lambda ^n 1)}(X)=0%$, then the interior has at most finite number of rational singularities. In particular, if X is Calabi–Yau of real dimension 5, then the vanishing of this invariant is equivalent to give the interior regularity up to normalization. Cohomology Group (dpeaa)DE-He213 Real Dimension (dpeaa)DE-He213 Pseudoconvex Domain (dpeaa)DE-He213 Holomorphic Vector Bundle (dpeaa)DE-He213 Coherent Sheaf (dpeaa)DE-He213 Gao, Yun aut Yau, Stephen aut Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 282(2015), 1-2 vom: 26. Okt., Seite 389-403 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:282 year:2015 number:1-2 day:26 month:10 pages:389-403 https://dx.doi.org/10.1007/s00209-015-1544-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 282 2015 1-2 26 10 389-403 |
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10.1007/s00209-015-1544-2 doi (DE-627)SPR001928066 (SPR)s00209-015-1544-2-e DE-627 ger DE-627 rakwb eng Du, Rong verfasserin aut On higher dimensional complex Plateau problem 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract Let X be a compact connected strongly pseudoconvex CR manifold of real dimension %$2n-1%$ in %${\mathbb {C}}^{N}%$. It has been an interesting question to find an intrinsic smoothness criteria for the complex Plateau problem. For %$n\ge 3%$ and %$N=n+1%$, Yau found a necessary and sufficient condition for the interior regularity of the Harvey–Lawson solution to the complex Plateau problem by means of Kohn–Rossi cohomology groups on X in 1981. For %$n=2%$ and %$N\ge n+1%$, the first and third authors introduced a new CR invariant %$g^{(1,1)}(X)%$ of X. The vanishing of this invariant will give the interior regularity of the Harvey–Lawson solution up to normalization. For %$n\ge 3%$ and %$N>n+1%$, the problem still remains open. In this paper, we generalize the invariant %$g^{(1,1)}(X)%$ to higher dimension as %$g^{(\Lambda ^n 1)}(X)%$ and show that if %$g^{(\Lambda ^n 1)}(X)=0%$, then the interior has at most finite number of rational singularities. In particular, if X is Calabi–Yau of real dimension 5, then the vanishing of this invariant is equivalent to give the interior regularity up to normalization. Cohomology Group (dpeaa)DE-He213 Real Dimension (dpeaa)DE-He213 Pseudoconvex Domain (dpeaa)DE-He213 Holomorphic Vector Bundle (dpeaa)DE-He213 Coherent Sheaf (dpeaa)DE-He213 Gao, Yun aut Yau, Stephen aut Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 282(2015), 1-2 vom: 26. Okt., Seite 389-403 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:282 year:2015 number:1-2 day:26 month:10 pages:389-403 https://dx.doi.org/10.1007/s00209-015-1544-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 282 2015 1-2 26 10 389-403 |
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10.1007/s00209-015-1544-2 doi (DE-627)SPR001928066 (SPR)s00209-015-1544-2-e DE-627 ger DE-627 rakwb eng Du, Rong verfasserin aut On higher dimensional complex Plateau problem 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract Let X be a compact connected strongly pseudoconvex CR manifold of real dimension %$2n-1%$ in %${\mathbb {C}}^{N}%$. It has been an interesting question to find an intrinsic smoothness criteria for the complex Plateau problem. For %$n\ge 3%$ and %$N=n+1%$, Yau found a necessary and sufficient condition for the interior regularity of the Harvey–Lawson solution to the complex Plateau problem by means of Kohn–Rossi cohomology groups on X in 1981. For %$n=2%$ and %$N\ge n+1%$, the first and third authors introduced a new CR invariant %$g^{(1,1)}(X)%$ of X. The vanishing of this invariant will give the interior regularity of the Harvey–Lawson solution up to normalization. For %$n\ge 3%$ and %$N>n+1%$, the problem still remains open. In this paper, we generalize the invariant %$g^{(1,1)}(X)%$ to higher dimension as %$g^{(\Lambda ^n 1)}(X)%$ and show that if %$g^{(\Lambda ^n 1)}(X)=0%$, then the interior has at most finite number of rational singularities. In particular, if X is Calabi–Yau of real dimension 5, then the vanishing of this invariant is equivalent to give the interior regularity up to normalization. Cohomology Group (dpeaa)DE-He213 Real Dimension (dpeaa)DE-He213 Pseudoconvex Domain (dpeaa)DE-He213 Holomorphic Vector Bundle (dpeaa)DE-He213 Coherent Sheaf (dpeaa)DE-He213 Gao, Yun aut Yau, Stephen aut Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 282(2015), 1-2 vom: 26. Okt., Seite 389-403 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:282 year:2015 number:1-2 day:26 month:10 pages:389-403 https://dx.doi.org/10.1007/s00209-015-1544-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 282 2015 1-2 26 10 389-403 |
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Enthalten in Mathematische Zeitschrift 282(2015), 1-2 vom: 26. Okt., Seite 389-403 volume:282 year:2015 number:1-2 day:26 month:10 pages:389-403 |
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It has been an interesting question to find an intrinsic smoothness criteria for the complex Plateau problem. For %$n\ge 3%$ and %$N=n+1%$, Yau found a necessary and sufficient condition for the interior regularity of the Harvey–Lawson solution to the complex Plateau problem by means of Kohn–Rossi cohomology groups on X in 1981. For %$n=2%$ and %$N\ge n+1%$, the first and third authors introduced a new CR invariant %$g^{(1,1)}(X)%$ of X. The vanishing of this invariant will give the interior regularity of the Harvey–Lawson solution up to normalization. For %$n\ge 3%$ and %$N>n+1%$, the problem still remains open. In this paper, we generalize the invariant %$g^{(1,1)}(X)%$ to higher dimension as %$g^{(\Lambda ^n 1)}(X)%$ and show that if %$g^{(\Lambda ^n 1)}(X)=0%$, then the interior has at most finite number of rational singularities. 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on higher dimensional complex plateau problem |
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On higher dimensional complex Plateau problem |
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Abstract Let X be a compact connected strongly pseudoconvex CR manifold of real dimension %$2n-1%$ in %${\mathbb {C}}^{N}%$. It has been an interesting question to find an intrinsic smoothness criteria for the complex Plateau problem. For %$n\ge 3%$ and %$N=n+1%$, Yau found a necessary and sufficient condition for the interior regularity of the Harvey–Lawson solution to the complex Plateau problem by means of Kohn–Rossi cohomology groups on X in 1981. For %$n=2%$ and %$N\ge n+1%$, the first and third authors introduced a new CR invariant %$g^{(1,1)}(X)%$ of X. The vanishing of this invariant will give the interior regularity of the Harvey–Lawson solution up to normalization. For %$n\ge 3%$ and %$N>n+1%$, the problem still remains open. In this paper, we generalize the invariant %$g^{(1,1)}(X)%$ to higher dimension as %$g^{(\Lambda ^n 1)}(X)%$ and show that if %$g^{(\Lambda ^n 1)}(X)=0%$, then the interior has at most finite number of rational singularities. In particular, if X is Calabi–Yau of real dimension 5, then the vanishing of this invariant is equivalent to give the interior regularity up to normalization. © Springer-Verlag Berlin Heidelberg 2015 |
| abstractGer |
Abstract Let X be a compact connected strongly pseudoconvex CR manifold of real dimension %$2n-1%$ in %${\mathbb {C}}^{N}%$. It has been an interesting question to find an intrinsic smoothness criteria for the complex Plateau problem. For %$n\ge 3%$ and %$N=n+1%$, Yau found a necessary and sufficient condition for the interior regularity of the Harvey–Lawson solution to the complex Plateau problem by means of Kohn–Rossi cohomology groups on X in 1981. For %$n=2%$ and %$N\ge n+1%$, the first and third authors introduced a new CR invariant %$g^{(1,1)}(X)%$ of X. The vanishing of this invariant will give the interior regularity of the Harvey–Lawson solution up to normalization. For %$n\ge 3%$ and %$N>n+1%$, the problem still remains open. In this paper, we generalize the invariant %$g^{(1,1)}(X)%$ to higher dimension as %$g^{(\Lambda ^n 1)}(X)%$ and show that if %$g^{(\Lambda ^n 1)}(X)=0%$, then the interior has at most finite number of rational singularities. In particular, if X is Calabi–Yau of real dimension 5, then the vanishing of this invariant is equivalent to give the interior regularity up to normalization. © Springer-Verlag Berlin Heidelberg 2015 |
| abstract_unstemmed |
Abstract Let X be a compact connected strongly pseudoconvex CR manifold of real dimension %$2n-1%$ in %${\mathbb {C}}^{N}%$. It has been an interesting question to find an intrinsic smoothness criteria for the complex Plateau problem. For %$n\ge 3%$ and %$N=n+1%$, Yau found a necessary and sufficient condition for the interior regularity of the Harvey–Lawson solution to the complex Plateau problem by means of Kohn–Rossi cohomology groups on X in 1981. For %$n=2%$ and %$N\ge n+1%$, the first and third authors introduced a new CR invariant %$g^{(1,1)}(X)%$ of X. The vanishing of this invariant will give the interior regularity of the Harvey–Lawson solution up to normalization. For %$n\ge 3%$ and %$N>n+1%$, the problem still remains open. In this paper, we generalize the invariant %$g^{(1,1)}(X)%$ to higher dimension as %$g^{(\Lambda ^n 1)}(X)%$ and show that if %$g^{(\Lambda ^n 1)}(X)=0%$, then the interior has at most finite number of rational singularities. In particular, if X is Calabi–Yau of real dimension 5, then the vanishing of this invariant is equivalent to give the interior regularity up to normalization. © Springer-Verlag Berlin Heidelberg 2015 |
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On higher dimensional complex Plateau problem |
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Gao, Yun Yau, Stephen |
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| score |
7.401534 |