On the existence of solutions to the Orlicz Aleksandrov problem

被引：0
|
作者：
Hu, Zejun [1 ]
Li, Hai [1 ]
机构：
[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China
来源：
GEOMETRIAE DEDICATA | 2023年 / 217卷 / 03期
基金：
美国国家科学基金会;
关键词：
Convex body; Orlicz Aleksandrov problem; Orlicz integral curvature; MINKOWSKI PROBLEM; GAUSS CURVATURE;
D O I：
10.1007/s10711-023-00794-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In [Int Math Res Not 7: 5492-5519 (2021)], Feng and He introduced the Orlicz Aleksandrov problem and proved that, there exists a convex body and an explicit constant, such that the problem is solved provided the given measure is even. In this paper, extending their results, we first prove that the desired convex body always exists for each constant in an interval. Then, we prove the existence of solutions to the problem for general measure that is not necessarily even.
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页数：11
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