On the Lp dual Minkowski problem

被引：91

作者：

Huang, Yong ^{[1
]}

Zhao, Yiming ^{[2
]}

机构：

[1] Hunan Univ, Inst Math, Changsha 410082, Hunan, Peoples R China

[2] NYU, Dept Math, Brooklyn, NY 11201 USA

来源：

ADVANCES IN MATHEMATICS | 2018年 / 332卷

关键词：

L-p dual Minkowski problem; L-p Minkowski problem; Dual Minkowski problem; Degenerate Monge-Ampere equation; Regularity; BUSEMANN-PETTY PROBLEM; INTERSECTION BODIES; SYMMETRIC-SOLUTIONS; SURFACE MEASURE; FIREY THEORY; AFFINE; VALUATIONS; REGULARITY; CLASSIFICATION; SPHERE;

D O I：

10.1016/j.aim.2018.05.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The (p), dual curvature measure was introduced by Lutwak, Yang & Zhang in an attempt to unify the L-p Brunn Minkowski theory and the dual Brunn-Minkowski theory. The characterization problem for L-p dual curvature measure, called the L-p dual Minkowski problem, is a fundamental problem in this unifying theory. The L-p dual Minkowski problem contains the L-p Minkowski problem and the dual Minkowski problem, two major problems in modern convex geometry that remain open in general. In this paper, existence results on the L-p dual Minkowski problem in the weak sense will be provided. Moreover, existence and uniqueness of the solution in the smooth category will also be demonstrated. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：57 / 84

页数：28