Inverse Gauss Curvature Flows and Orlicz Minkowski Problem

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2022-01-01 DOI:10.1515/agms-2022-0146

Bin Chen, Jingshi Cui, P. Zhao

引用次数: 0

Abstract

Abstract Liu and Lu [27] investigated a generalized Gauss curvature flow and obtained an even solution to the dual Orlicz-Minkowski problem under some appropriate assumptions. The present paper investigates a inverse Gauss curvature flow, and achieves the long-time existence and convergence of this flow via a different C0-estimate technique under weaker conditions. As an application of this inverse Gauss curvature flow, the present paper first arrives at a non-even smooth solution to the Orlicz Minkowski problem.

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逆高斯曲率流与Orlicz Minkowski问题

Liu和Lu研究了广义高斯曲率流，在适当的假设条件下得到了对偶Orlicz-Minkowski问题的偶解。本文研究了一种反高斯曲率流，在较弱的条件下，通过一种不同的c0估计技术，得到了该流的长时间存在性和收敛性。作为逆高斯曲率流的一个应用，本文首先得到了Orlicz Minkowski问题的非均匀光滑解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.