A flow approach to the Musielak-Orlicz-Gauss image problem

被引：11
|
作者：
Li, Qi-Rui [1 ]
Sheng, Weimin [1 ]
Ye, Deping [2 ]
Yi, Caihong [3 ]
机构：
[1] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Peoples R China
[2] Memorial Univ Newfoundland, Dept Math & Stat, St John, NL A1C 5S7, Canada
[3] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Peoples R China
来源：
ADVANCES IN MATHEMATICS | 2022年 / 403卷
基金：
加拿大自然科学与工程研究理事会;
关键词：
Gauss image problem; Geometric flows; Monge-Ampere equation; Musielak-Orlicz addition; Orlicz-Minkowski problem; BRUNN-MINKOWSKI THEORY; ALEKSANDROV PROBLEM; CURVATURE;
D O I：
10.1016/j.aim.2022.108379
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, the extended Musielak-Orlicz-Gauss image problem is studied. Such a problem aims to characterize the Musielak-Orlicz-Gauss image measure C?G,psi,lambda(12, & BULL;) of convex body 12 in Rn+1 containing the origin (but the origin is not necessary in its interior). In particular, we provide solutions to the extended Musielak-Orlicz-Gauss image problem based on the study of suitably designed parabolic flows, and by the use of approximation technique (for general measures). Our parabolic flows involve two Musielak-Orlicz functions and hence contain many well-studied curvature flows related to Minkowski type problems as special cases. Our results not only generalize many previously known solutions to the Minkowski type and Gauss image problems, but also provide solutions to those problems in many unsolved cases. (c) 2022 Elsevier Inc. All rights reserved.
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页数：40
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