Affine complete locally convex hypersurfaces

Neil S. Trudinger; Xu Jia Wang

doi:10.1007/s00222-002-0229-8

Affine complete locally convex hypersurfaces

Neil S. Trudinger^*
, Xu Jia Wang

^*Corresponding author for this work

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

47 Citations (Scopus)

Abstract

An open problem in affine geometry is whether an affine complete locally uniformly convex hypersurface in Euclidean (n + 1)-space is Euclidean complete for n ≥ 2. In this paper we give the affirmative answer. As an application, it follows that an affine complete, affine maximal surface in R³ must be an elliptic paraboloid.

Original language	English
Pages (from-to)	45-60
Number of pages	16
Journal	Inventiones Mathematicae
Volume	150
Issue number	1
DOIs	https://doi.org/10.1007/s00222-002-0229-8
Publication status	Published - 2002

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AB - An open problem in affine geometry is whether an affine complete locally uniformly convex hypersurface in Euclidean (n + 1)-space is Euclidean complete for n ≥ 2. In this paper we give the affirmative answer. As an application, it follows that an affine complete, affine maximal surface in R3 must be an elliptic paraboloid.

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JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

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Affine complete locally convex hypersurfaces

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