Centroaffine Bernstein problems
type: Item
instance of: scholarly article
title: Centroaffine Bernstein problems
zbMATH Open document ID: 1062.53005
author: An-Min Li
author: Haizhong Li
author: Udo Simon
published in: Differential Geometry and its Applications
publication date: 2004-08-16T00:00:00Z
review text: The authors study the fourth-order equation associated with the Bernstein problems in global centroaffine differential geometry. They summarize basic formulas of centroaffine hypersurfaces theory in terms of Cartan's moving frames and give examples of extremal and complete centroaffine hypersurfaces. A list of problems and conjectures is given with partial solutions.
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 49Q05
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 2091330
zbMATH Keywords: centroaffine extremal hypersurfaces
zbMATH Keywords: centroaffine Bernstein problem
zbMATH Keywords: affine spheres
reviewed by: Bernard Rouxel
MaRDI profile type: Publication
full work available at URL: j.difgeo.2003.12.004
OpenAlex ID: W2066560233
Wikidata QID: Q115358081
cites work: Convex affine maximal surfaces
cites work: Hypersurfaces with Maximal Affinely Invariant Area
cites work: Q3881477
cites work: Q3948276
cites work: The Calabi conjecture on affine maximal surfaces
cites work: Euclidean complete affine surfaces with constant affine mean curvature
cites work: Q4781385
cites work: A Bernstein property of affine maximal hypersurfaces
cites work: Cubic form methods and relative Tchebychev hypersurfaces
cites work: Q4342826
cites work: Global affine differential geometry of hypersurfaces
cites work: Hypersurfaces with prescribed affine Gauss-Kronecker curvature
cites work: Canonical centroaffine hypersurfaces in \({\mathbb{R}{}}^{n+1}\)
cites work: The centroaffine Tchebychev operator
cites work: Centroaffine surfaces with parallel traceless cubic form
cites work: Q4028202
cites work: Isometric immersions of Riemannian manifolds
cites work: Q4760324
cites work: Curvature estimates for minimal hypersurfaces
cites work: Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature
cites work: Q4838145
cites work: The Bernstein problem for affine maximal hypersurfaces
cites work: Centroaffine minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
cites work: Harmonic functions on complete riemannian manifolds
cites work: Q4102442
DOI: 10.1016/J.DIFGEO.2003.12.004
description: scientific article; zbMATH DE number 2091330