Enclosed convex hypersurfaces with maximal affine area

Weimin Sheng; Neil S. Trudinger; Xu Jia Wang

doi:10.1007/s00209-005-0862-1

Enclosed convex hypersurfaces with maximal affine area

Weimin Sheng^*, Neil S. Trudinger, Xu Jia Wang

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

In this paper we study the regularity of closed, convex surfaces which achieve maximal affine area among all the closed, convex surfaces enclosed in a given domain in the Euclidean 3-space. We prove the C ^1, ^α regularity for general domains and C ^1,1 regularity if the domain is uniformly convex.

Original language	English
Pages (from-to)	497-510
Number of pages	14
Journal	Mathematische Zeitschrift
Volume	252
Issue number	3
DOIs	https://doi.org/10.1007/s00209-005-0862-1
Publication status	Published - Mar 2006

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title = "Enclosed convex hypersurfaces with maximal affine area",

abstract = "In this paper we study the regularity of closed, convex surfaces which achieve maximal affine area among all the closed, convex surfaces enclosed in a given domain in the Euclidean 3-space. We prove the C 1, α regularity for general domains and C 1,1 regularity if the domain is uniformly convex.",

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

year = "2006",

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T1 - Enclosed convex hypersurfaces with maximal affine area

AU - Sheng, Weimin

AU - Trudinger, Neil S.

AU - Wang, Xu Jia

PY - 2006/3

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N2 - In this paper we study the regularity of closed, convex surfaces which achieve maximal affine area among all the closed, convex surfaces enclosed in a given domain in the Euclidean 3-space. We prove the C 1, α regularity for general domains and C 1,1 regularity if the domain is uniformly convex.

AB - In this paper we study the regularity of closed, convex surfaces which achieve maximal affine area among all the closed, convex surfaces enclosed in a given domain in the Euclidean 3-space. We prove the C 1, α regularity for general domains and C 1,1 regularity if the domain is uniformly convex.

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U2 - 10.1007/s00209-005-0862-1

DO - 10.1007/s00209-005-0862-1

M3 - Article

SN - 0025-5874

VL - 252

SP - 497

EP - 510

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3

ER -

Enclosed convex hypersurfaces with maximal affine area

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