Mathematics

CLC number: O186

The Existence of Solution to the Even Orlicz Chord Minkowski Problem

偶Orlicz弦Minkowski问题解的存在性

¹ School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China
² Department of Mathematics, Shanghai University, Shanghai 200444, China

^† Corresponding author. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 16 May 2024

Abstract

Chord measures are newly discovered translation-invariant geometric measures of convex bodies in ${\mathbb{R}}^n$ by Lutwak-Xi-Yang-Zhang (Communications on Pure and Applied Mathematics, 2024), which is an extension of the surface area measure. The Minkowski problems for chord measures was considered by Lutwak-Xi-Yang-Zhang. In this paper, we use variational method to solve the even Orlicz chord Minkowski problem. The obtained results are an extension of the even Orlicz Minkowski problem from Haberl-Lutwak-Yang-Zhang (Advances in Mathematics, 2010 ).

摘要

2024年，Lutwak等人引入凸体的弦测度 (Communications on Pure and Applied Mathematics, 2024)。经典的表面积测度是一种特殊的弦测度。关于弦测度的Minkowski问题是凸几何中新的研究热点。本文采用变分方法研究Orlicz情形下偶弦测度的Minkowski问题解的存在性，所得到的结果是Haberl-Lutwak-Yang-Zhang (Advances in Mathematics, 2010) 关于偶表面积测度的Orlicz Minkowski问题的推广。