On locally convex hypersurfaces with boundary

Neil S. Trudinger; Xu Jia Wang

doi:10.1515/crll.2002.078

On locally convex hypersurfaces with boundary

Neil S. Trudinger^*, Xu Jia Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

35 Citations (SciVal)

Abstract

In this paper we give some geometric characterizations of locally convex hypersurfaces. In particular, we prove that for a given locally convex hypersurface M with boundary, there exists r > 0 depending only on the diameter of M and the principal curvatures of M on its boundary, such that the r-neighbourhood of any given point on M is convex. As an application we prove an existence theorem for a Plateau problem for locally convex hypersurfaces of constant Gauss curvature.

Original language	English
Pages (from-to)	11-32
Number of pages	22
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	551
DOIs	https://doi.org/10.1515/crll.2002.078
Publication status	Published - 2002

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10.1515/crll.2002.078

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title = "On locally convex hypersurfaces with boundary",

abstract = "In this paper we give some geometric characterizations of locally convex hypersurfaces. In particular, we prove that for a given locally convex hypersurface M with boundary, there exists r > 0 depending only on the diameter of M and the principal curvatures of M on its boundary, such that the r-neighbourhood of any given point on M is convex. As an application we prove an existence theorem for a Plateau problem for locally convex hypersurfaces of constant Gauss curvature.",

author = "Trudinger, {Neil S.} and Wang, {Xu Jia}",

year = "2002",

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AU - Wang, Xu Jia

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AB - In this paper we give some geometric characterizations of locally convex hypersurfaces. In particular, we prove that for a given locally convex hypersurface M with boundary, there exists r > 0 depending only on the diameter of M and the principal curvatures of M on its boundary, such that the r-neighbourhood of any given point on M is convex. As an application we prove an existence theorem for a Plateau problem for locally convex hypersurfaces of constant Gauss curvature.

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DO - 10.1515/crll.2002.078

M3 - Article

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EP - 32

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

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ER -

On locally convex hypersurfaces with boundary

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