Existence of convex hypersurfaces with prescribed centroaffine curvature-Reference-Cited by-同舟云学术

Existence of convex hypersurfaces with prescribed centroaffine curvature

Published:2023-11-07 Issue:2 Volume:377 Page:841-862
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Guang Qiang,Li Qi-Rui,Wang Xu-Jia

Abstract

In this paper, we study the existence of solutions to the centroaffine Minkowski problem, namely the existence of closed convex hypersurfaces in the Euclidean space R n + 1 \mathbb {R}^{n+1} with prescribed centroaffine curvature. This problem can be described as a variational problem with a functional resembling Kantorovich’s dual functional in optimal transportation. By using the Gauss curvature flow, we obtain new conditions for the existence of solutions to the problem.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/tran/2024-377-02/S0002-9947-2023-08881-X/S0002-9947-2023-08881-X.pdf

Reference26 articles.

1. Self-similar solutions for the anisotropic affine curve shortening problem;Ai, Jun;Calc. Var. Partial Differential Equations,2001

2. Axioms and fundamental equations of image processing;Alvarez, Luis;Arch. Rational Mech. Anal.,1993

3. Contraction of convex hypersurfaces by their affine normal;Andrews, Ben;J. Differential Geom.,1996

4. Classification of limiting shapes for isotropic curve flows;Andrews, Ben;J. Amer. Math. Soc.,2003

5. On the affine heat equation for non-convex curves;Angenent, Sigurd;J. Amer. Math. Soc.,1998

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On the functional ∫_Ωf + ∫_Ω*g;Advanced Nonlinear Studies;2024-02-01