Generalized connected sum construction for scalar flat metrics

Abstract In this paper we construct constant scalar curvature metrics on the generalized connected sum $${M = M_1 \, \sharp_K \, M_2}$$ of two compact Riemannian scalar flat manifolds (M1, g1) and (M2, g2) along a common Riemannian submanifold (K, gK) whose codimension is ≥3. Here we present two con...
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Autor*in:	Mazzieri, Lorenzo [verfasserIn]

Format:	Artikel
Sprache:	Englisch

Erschienen:	2009

Systematik:	SA 6730 SA 6730

Anmerkung:	© The Author(s) 2009

Übergeordnetes Werk:	Enthalten in: Manuscripta mathematica - Springer-Verlag, 1969, 129(2009), 2 vom: 10. Feb., Seite 137-168
Übergeordnetes Werk:	volume:129 ; year:2009 ; number:2 ; day:10 ; month:02 ; pages:137-168

Links:	Volltext

DOI / URN:	10.1007/s00229-009-0250-y

Katalog-ID:	OLC2061289304

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520			\|a Abstract In this paper we construct constant scalar curvature metrics on the generalized connected sum $${M = M_1 \, \sharp_K \, M_2}$$ of two compact Riemannian scalar flat manifolds (M1, g1) and (M2, g2) along a common Riemannian submanifold (K, gK) whose codimension is ≥3. Here we present two constructions: the first one produces a family of “small” (in general nonzero) constant scalar curvature metrics on the generalized connected sum of M1 and M2. It yields an extension of Joyce’s result for point-wise connected sums in the spirit of our previous issues for nonzero constant scalar curvature metrics. When the initial manifolds are not Ricci flat, and in particular they belong to the ($ 1_{+} $) class in the Kazdan–Warner classification, we refine the first construction in order to produce a family of scalar flat metrics on M. As a consequence we get new solutions to the Einstein constraint equations on the generalized connected sum of two compact time symmetric initial data sets, extending the Isenberg–Mazzeo–Pollack gluing construction.
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allfields	10.1007/s00229-009-0250-y doi (DE-627)OLC2061289304 (DE-He213)s00229-009-0250-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 6730 VZ rvk SA 6730 VZ rvk Mazzieri, Lorenzo verfasserin aut Generalized connected sum construction for scalar flat metrics 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2009 Abstract In this paper we construct constant scalar curvature metrics on the generalized connected sum $${M = M_1 \, \sharp_K \, M_2}$$ of two compact Riemannian scalar flat manifolds (M1, g1) and (M2, g2) along a common Riemannian submanifold (K, gK) whose codimension is ≥3. Here we present two constructions: the first one produces a family of “small” (in general nonzero) constant scalar curvature metrics on the generalized connected sum of M1 and M2. It yields an extension of Joyce’s result for point-wise connected sums in the spirit of our previous issues for nonzero constant scalar curvature metrics. When the initial manifolds are not Ricci flat, and in particular they belong to the ($ 1_{+} $) class in the Kazdan–Warner classification, we refine the first construction in order to produce a family of scalar flat metrics on M. As a consequence we get new solutions to the Einstein constraint equations on the generalized connected sum of two compact time symmetric initial data sets, extending the Isenberg–Mazzeo–Pollack gluing construction. Enthalten in Manuscripta mathematica Springer-Verlag, 1969 129(2009), 2 vom: 10. Feb., Seite 137-168 (DE-627)129081388 (DE-600)3448-4 (DE-576)014414244 0025-2611 nnns volume:129 year:2009 number:2 day:10 month:02 pages:137-168 https://doi.org/10.1007/s00229-009-0250-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4029 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4313 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 SA 6730 SA 6730 AR 129 2009 2 10 02 137-168
spelling	10.1007/s00229-009-0250-y doi (DE-627)OLC2061289304 (DE-He213)s00229-009-0250-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 6730 VZ rvk SA 6730 VZ rvk Mazzieri, Lorenzo verfasserin aut Generalized connected sum construction for scalar flat metrics 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2009 Abstract In this paper we construct constant scalar curvature metrics on the generalized connected sum $${M = M_1 \, \sharp_K \, M_2}$$ of two compact Riemannian scalar flat manifolds (M1, g1) and (M2, g2) along a common Riemannian submanifold (K, gK) whose codimension is ≥3. Here we present two constructions: the first one produces a family of “small” (in general nonzero) constant scalar curvature metrics on the generalized connected sum of M1 and M2. It yields an extension of Joyce’s result for point-wise connected sums in the spirit of our previous issues for nonzero constant scalar curvature metrics. When the initial manifolds are not Ricci flat, and in particular they belong to the ($ 1_{+} $) class in the Kazdan–Warner classification, we refine the first construction in order to produce a family of scalar flat metrics on M. As a consequence we get new solutions to the Einstein constraint equations on the generalized connected sum of two compact time symmetric initial data sets, extending the Isenberg–Mazzeo–Pollack gluing construction. Enthalten in Manuscripta mathematica Springer-Verlag, 1969 129(2009), 2 vom: 10. Feb., Seite 137-168 (DE-627)129081388 (DE-600)3448-4 (DE-576)014414244 0025-2611 nnns volume:129 year:2009 number:2 day:10 month:02 pages:137-168 https://doi.org/10.1007/s00229-009-0250-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4029 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4313 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 SA 6730 SA 6730 AR 129 2009 2 10 02 137-168
allfields_unstemmed	10.1007/s00229-009-0250-y doi (DE-627)OLC2061289304 (DE-He213)s00229-009-0250-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 6730 VZ rvk SA 6730 VZ rvk Mazzieri, Lorenzo verfasserin aut Generalized connected sum construction for scalar flat metrics 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2009 Abstract In this paper we construct constant scalar curvature metrics on the generalized connected sum $${M = M_1 \, \sharp_K \, M_2}$$ of two compact Riemannian scalar flat manifolds (M1, g1) and (M2, g2) along a common Riemannian submanifold (K, gK) whose codimension is ≥3. Here we present two constructions: the first one produces a family of “small” (in general nonzero) constant scalar curvature metrics on the generalized connected sum of M1 and M2. It yields an extension of Joyce’s result for point-wise connected sums in the spirit of our previous issues for nonzero constant scalar curvature metrics. When the initial manifolds are not Ricci flat, and in particular they belong to the ($ 1_{+} $) class in the Kazdan–Warner classification, we refine the first construction in order to produce a family of scalar flat metrics on M. As a consequence we get new solutions to the Einstein constraint equations on the generalized connected sum of two compact time symmetric initial data sets, extending the Isenberg–Mazzeo–Pollack gluing construction. Enthalten in Manuscripta mathematica Springer-Verlag, 1969 129(2009), 2 vom: 10. Feb., Seite 137-168 (DE-627)129081388 (DE-600)3448-4 (DE-576)014414244 0025-2611 nnns volume:129 year:2009 number:2 day:10 month:02 pages:137-168 https://doi.org/10.1007/s00229-009-0250-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4029 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4313 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 SA 6730 SA 6730 AR 129 2009 2 10 02 137-168
allfieldsGer	10.1007/s00229-009-0250-y doi (DE-627)OLC2061289304 (DE-He213)s00229-009-0250-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 6730 VZ rvk SA 6730 VZ rvk Mazzieri, Lorenzo verfasserin aut Generalized connected sum construction for scalar flat metrics 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2009 Abstract In this paper we construct constant scalar curvature metrics on the generalized connected sum $${M = M_1 \, \sharp_K \, M_2}$$ of two compact Riemannian scalar flat manifolds (M1, g1) and (M2, g2) along a common Riemannian submanifold (K, gK) whose codimension is ≥3. Here we present two constructions: the first one produces a family of “small” (in general nonzero) constant scalar curvature metrics on the generalized connected sum of M1 and M2. It yields an extension of Joyce’s result for point-wise connected sums in the spirit of our previous issues for nonzero constant scalar curvature metrics. When the initial manifolds are not Ricci flat, and in particular they belong to the ($ 1_{+} $) class in the Kazdan–Warner classification, we refine the first construction in order to produce a family of scalar flat metrics on M. As a consequence we get new solutions to the Einstein constraint equations on the generalized connected sum of two compact time symmetric initial data sets, extending the Isenberg–Mazzeo–Pollack gluing construction. Enthalten in Manuscripta mathematica Springer-Verlag, 1969 129(2009), 2 vom: 10. Feb., Seite 137-168 (DE-627)129081388 (DE-600)3448-4 (DE-576)014414244 0025-2611 nnns volume:129 year:2009 number:2 day:10 month:02 pages:137-168 https://doi.org/10.1007/s00229-009-0250-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4029 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4313 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 SA 6730 SA 6730 AR 129 2009 2 10 02 137-168
allfieldsSound	10.1007/s00229-009-0250-y doi (DE-627)OLC2061289304 (DE-He213)s00229-009-0250-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 6730 VZ rvk SA 6730 VZ rvk Mazzieri, Lorenzo verfasserin aut Generalized connected sum construction for scalar flat metrics 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2009 Abstract In this paper we construct constant scalar curvature metrics on the generalized connected sum $${M = M_1 \, \sharp_K \, M_2}$$ of two compact Riemannian scalar flat manifolds (M1, g1) and (M2, g2) along a common Riemannian submanifold (K, gK) whose codimension is ≥3. Here we present two constructions: the first one produces a family of “small” (in general nonzero) constant scalar curvature metrics on the generalized connected sum of M1 and M2. It yields an extension of Joyce’s result for point-wise connected sums in the spirit of our previous issues for nonzero constant scalar curvature metrics. When the initial manifolds are not Ricci flat, and in particular they belong to the ($ 1_{+} $) class in the Kazdan–Warner classification, we refine the first construction in order to produce a family of scalar flat metrics on M. As a consequence we get new solutions to the Einstein constraint equations on the generalized connected sum of two compact time symmetric initial data sets, extending the Isenberg–Mazzeo–Pollack gluing construction. Enthalten in Manuscripta mathematica Springer-Verlag, 1969 129(2009), 2 vom: 10. Feb., Seite 137-168 (DE-627)129081388 (DE-600)3448-4 (DE-576)014414244 0025-2611 nnns volume:129 year:2009 number:2 day:10 month:02 pages:137-168 https://doi.org/10.1007/s00229-009-0250-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4029 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4313 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 SA 6730 SA 6730 AR 129 2009 2 10 02 137-168
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author	Mazzieri, Lorenzo
spellingShingle	Mazzieri, Lorenzo ddc 510 ssgn 17,1 rvk SA 6730 Generalized connected sum construction for scalar flat metrics
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topic_title	510 VZ 17,1 ssgn SA 6730 VZ rvk Generalized connected sum construction for scalar flat metrics
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title	Generalized connected sum construction for scalar flat metrics
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title_full	Generalized connected sum construction for scalar flat metrics
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title_sort	generalized connected sum construction for scalar flat metrics
title_auth	Generalized connected sum construction for scalar flat metrics
abstract	Abstract In this paper we construct constant scalar curvature metrics on the generalized connected sum $${M = M_1 \, \sharp_K \, M_2}$$ of two compact Riemannian scalar flat manifolds (M1, g1) and (M2, g2) along a common Riemannian submanifold (K, gK) whose codimension is ≥3. Here we present two constructions: the first one produces a family of “small” (in general nonzero) constant scalar curvature metrics on the generalized connected sum of M1 and M2. It yields an extension of Joyce’s result for point-wise connected sums in the spirit of our previous issues for nonzero constant scalar curvature metrics. When the initial manifolds are not Ricci flat, and in particular they belong to the ($ 1_{+} $) class in the Kazdan–Warner classification, we refine the first construction in order to produce a family of scalar flat metrics on M. As a consequence we get new solutions to the Einstein constraint equations on the generalized connected sum of two compact time symmetric initial data sets, extending the Isenberg–Mazzeo–Pollack gluing construction. © The Author(s) 2009
abstractGer	Abstract In this paper we construct constant scalar curvature metrics on the generalized connected sum $${M = M_1 \, \sharp_K \, M_2}$$ of two compact Riemannian scalar flat manifolds (M1, g1) and (M2, g2) along a common Riemannian submanifold (K, gK) whose codimension is ≥3. Here we present two constructions: the first one produces a family of “small” (in general nonzero) constant scalar curvature metrics on the generalized connected sum of M1 and M2. It yields an extension of Joyce’s result for point-wise connected sums in the spirit of our previous issues for nonzero constant scalar curvature metrics. When the initial manifolds are not Ricci flat, and in particular they belong to the ($ 1_{+} $) class in the Kazdan–Warner classification, we refine the first construction in order to produce a family of scalar flat metrics on M. As a consequence we get new solutions to the Einstein constraint equations on the generalized connected sum of two compact time symmetric initial data sets, extending the Isenberg–Mazzeo–Pollack gluing construction. © The Author(s) 2009
abstract_unstemmed	Abstract In this paper we construct constant scalar curvature metrics on the generalized connected sum $${M = M_1 \, \sharp_K \, M_2}$$ of two compact Riemannian scalar flat manifolds (M1, g1) and (M2, g2) along a common Riemannian submanifold (K, gK) whose codimension is ≥3. Here we present two constructions: the first one produces a family of “small” (in general nonzero) constant scalar curvature metrics on the generalized connected sum of M1 and M2. It yields an extension of Joyce’s result for point-wise connected sums in the spirit of our previous issues for nonzero constant scalar curvature metrics. When the initial manifolds are not Ricci flat, and in particular they belong to the ($ 1_{+} $) class in the Kazdan–Warner classification, we refine the first construction in order to produce a family of scalar flat metrics on M. As a consequence we get new solutions to the Einstein constraint equations on the generalized connected sum of two compact time symmetric initial data sets, extending the Isenberg–Mazzeo–Pollack gluing construction. © The Author(s) 2009
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title_short	Generalized connected sum construction for scalar flat metrics
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