Stable anisotropic minimal hypersurfaces in $\mathbf {R}^{4}$

We show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in $\mathbf {R}^4$ has intrinsic cubic volume growth, provided the parametric elliptic integral is $C^2$ -close to the area functional. We also obtain an interior volume upper bound for stable anisotropic...
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Gespeichert in:

Autor*in:	Otis Chodosh [verfasserIn] Chao Li [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	53C42 35J50 53A10 49F10

Übergeordnetes Werk:	In: Forum of Mathematics, Pi - Cambridge University Press, 2017, 11(2023)
Übergeordnetes Werk:	volume:11 ; year:2023

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1017/fmp.2023.1

Katalog-ID:	DOAJ088111857

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spelling	10.1017/fmp.2023.1 doi (DE-627)DOAJ088111857 (DE-599)DOAJb74c876d146f4476aec343bd794c943e DE-627 ger DE-627 rakwb eng QA1-939 Otis Chodosh verfasserin aut Stable anisotropic minimal hypersurfaces in $\mathbf {R}^{4}$ 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in $\mathbf {R}^4$ has intrinsic cubic volume growth, provided the parametric elliptic integral is $C^2$ -close to the area functional. We also obtain an interior volume upper bound for stable anisotropic minimal hypersurfaces in the unit ball. We can estimate the constants explicitly in all of our results. In particular, this paper gives an alternative proof of our recent stable Bernstein theorem for minimal hypersurfaces in $\mathbf {R}^4$ . The new proof is more closely related to techniques from the study of strictly positive scalar curvature. 53C42 35J50 53A10 49F10 Mathematics Chao Li verfasserin aut In Forum of Mathematics, Pi Cambridge University Press, 2017 11(2023) (DE-627)751861073 (DE-600)2723153-7 20505086 nnns volume:11 year:2023 https://doi.org/10.1017/fmp.2023.1 kostenfrei https://doaj.org/article/b74c876d146f4476aec343bd794c943e kostenfrei https://www.cambridge.org/core/product/identifier/S205050862300001X/type/journal_article kostenfrei https://doaj.org/toc/2050-5086 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023
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allfieldsGer	10.1017/fmp.2023.1 doi (DE-627)DOAJ088111857 (DE-599)DOAJb74c876d146f4476aec343bd794c943e DE-627 ger DE-627 rakwb eng QA1-939 Otis Chodosh verfasserin aut Stable anisotropic minimal hypersurfaces in $\mathbf {R}^{4}$ 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in $\mathbf {R}^4$ has intrinsic cubic volume growth, provided the parametric elliptic integral is $C^2$ -close to the area functional. We also obtain an interior volume upper bound for stable anisotropic minimal hypersurfaces in the unit ball. We can estimate the constants explicitly in all of our results. In particular, this paper gives an alternative proof of our recent stable Bernstein theorem for minimal hypersurfaces in $\mathbf {R}^4$ . The new proof is more closely related to techniques from the study of strictly positive scalar curvature. 53C42 35J50 53A10 49F10 Mathematics Chao Li verfasserin aut In Forum of Mathematics, Pi Cambridge University Press, 2017 11(2023) (DE-627)751861073 (DE-600)2723153-7 20505086 nnns volume:11 year:2023 https://doi.org/10.1017/fmp.2023.1 kostenfrei https://doaj.org/article/b74c876d146f4476aec343bd794c943e kostenfrei https://www.cambridge.org/core/product/identifier/S205050862300001X/type/journal_article kostenfrei https://doaj.org/toc/2050-5086 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023
allfieldsSound	10.1017/fmp.2023.1 doi (DE-627)DOAJ088111857 (DE-599)DOAJb74c876d146f4476aec343bd794c943e DE-627 ger DE-627 rakwb eng QA1-939 Otis Chodosh verfasserin aut Stable anisotropic minimal hypersurfaces in $\mathbf {R}^{4}$ 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in $\mathbf {R}^4$ has intrinsic cubic volume growth, provided the parametric elliptic integral is $C^2$ -close to the area functional. We also obtain an interior volume upper bound for stable anisotropic minimal hypersurfaces in the unit ball. We can estimate the constants explicitly in all of our results. In particular, this paper gives an alternative proof of our recent stable Bernstein theorem for minimal hypersurfaces in $\mathbf {R}^4$ . The new proof is more closely related to techniques from the study of strictly positive scalar curvature. 53C42 35J50 53A10 49F10 Mathematics Chao Li verfasserin aut In Forum of Mathematics, Pi Cambridge University Press, 2017 11(2023) (DE-627)751861073 (DE-600)2723153-7 20505086 nnns volume:11 year:2023 https://doi.org/10.1017/fmp.2023.1 kostenfrei https://doaj.org/article/b74c876d146f4476aec343bd794c943e kostenfrei https://www.cambridge.org/core/product/identifier/S205050862300001X/type/journal_article kostenfrei https://doaj.org/toc/2050-5086 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023
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callnumber-first	Q - Science
author	Otis Chodosh
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title	Stable anisotropic minimal hypersurfaces in $\mathbf {R}^{4}$
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title_sort	stable anisotropic minimal hypersurfaces in $\mathbf {r}^{4}$
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title_auth	Stable anisotropic minimal hypersurfaces in $\mathbf {R}^{4}$
abstract	We show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in $\mathbf {R}^4$ has intrinsic cubic volume growth, provided the parametric elliptic integral is $C^2$ -close to the area functional. We also obtain an interior volume upper bound for stable anisotropic minimal hypersurfaces in the unit ball. We can estimate the constants explicitly in all of our results. In particular, this paper gives an alternative proof of our recent stable Bernstein theorem for minimal hypersurfaces in $\mathbf {R}^4$ . The new proof is more closely related to techniques from the study of strictly positive scalar curvature.
abstractGer	We show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in $\mathbf {R}^4$ has intrinsic cubic volume growth, provided the parametric elliptic integral is $C^2$ -close to the area functional. We also obtain an interior volume upper bound for stable anisotropic minimal hypersurfaces in the unit ball. We can estimate the constants explicitly in all of our results. In particular, this paper gives an alternative proof of our recent stable Bernstein theorem for minimal hypersurfaces in $\mathbf {R}^4$ . The new proof is more closely related to techniques from the study of strictly positive scalar curvature.
abstract_unstemmed	We show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in $\mathbf {R}^4$ has intrinsic cubic volume growth, provided the parametric elliptic integral is $C^2$ -close to the area functional. We also obtain an interior volume upper bound for stable anisotropic minimal hypersurfaces in the unit ball. We can estimate the constants explicitly in all of our results. In particular, this paper gives an alternative proof of our recent stable Bernstein theorem for minimal hypersurfaces in $\mathbf {R}^4$ . The new proof is more closely related to techniques from the study of strictly positive scalar curvature.
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title_short	Stable anisotropic minimal hypersurfaces in $\mathbf {R}^{4}$
url	https://doi.org/10.1017/fmp.2023.1 https://doaj.org/article/b74c876d146f4476aec343bd794c943e https://www.cambridge.org/core/product/identifier/S205050862300001X/type/journal_article https://doaj.org/toc/2050-5086
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score	7.4005327

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Stable anisotropic minimal hypersurfaces in $\mathbf {R}^{4}$

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