The planar Orlicz Minkowski problem in the L1-sense

被引：26
|
作者：
Yijing, Sun [1 ]
Yiming, Long [2 ,3 ]
机构：
[1] Univ Chinese Acad Sci, Dept Math, Beijing 100049, Peoples R China
[2] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China
[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China
来源：
ADVANCES IN MATHEMATICS | 2015年 / 281卷
关键词：
Minkowski problem; Negative powers; Variational method; FIREY THEORY; AFFINE; SURFACE; CLASSIFICATION; REGULARITY; CURVATURE;
D O I：
10.1016/j.aim.2015.03.032
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we solve L-p Minkowski problem for L-1 data and all p < 0, and Orlicz Minkowski problem with two nonlinear terms in L-1 sense. A byproduct is the Blaschke-Santalo inequality, which was previously established for only constant data, and now is shown to hold for L-1 data. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：1364 / 1383
页数：20
相关论文
共 50 条
  • [1] The Planar Orlicz Minkowski Problem for p=0 Without Even Assumptions
    Sun Yijing
    Zhang Duanzhi
    JOURNAL OF GEOMETRIC ANALYSIS, 2019, 29 (04) : 3384 - 3404
  • [2] On the Orlicz Minkowski Problem for Polytopes
    Huang, Qingzhong
    He, Binwu
    DISCRETE & COMPUTATIONAL GEOMETRY, 2012, 48 (02) : 281 - 297
  • [3] The even Orlicz Minkowski problem
    Haberl, Christoph
    Lutwak, Erwin
    Yang, Deane
    Zhang, Gaoyong
    ADVANCES IN MATHEMATICS, 2010, 224 (06) : 2485 - 2510
  • [4] The Dual Orlicz–Minkowski Problem
    Baocheng Zhu
    Sudan Xing
    Deping Ye
    The Journal of Geometric Analysis, 2018, 28 : 3829 - 3855
  • [5] On the Orlicz Minkowski Problem for Polytopes
    Qingzhong Huang
    Binwu He
    Discrete & Computational Geometry, 2012, 48 : 281 - 297
  • [6] ON THE DISCRETE ORLICZ MINKOWSKI PROBLEM
    Wu, Yuchi
    Xi, Dongmeng
    Leng, Gangsong
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 371 (03) : 1795 - 1814
  • [7] On the discrete Orlicz Minkowski problem II
    Yuchi Wu
    Dongmeng Xi
    Gangsong Leng
    Geometriae Dedicata, 2020, 205 : 177 - 190
  • [8] On the Orlicz Minkowski problem for logarithmic capacity
    Hu, Zejun
    Li, Hai
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 510 (01)
  • [9] THE ORLICZ MINKOWSKI PROBLEM FOR GENERAL MEASURES
    Xie, Fengfan
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 150 (10) : 4433 - 4445
  • [10] The Dual Orlicz-Minkowski Problem
    Zhu, Baocheng
    Xing, Sudan
    Ye, Deping
    JOURNAL OF GEOMETRIC ANALYSIS, 2018, 28 (04) : 3829 - 3855
12345