The discrete horospherical p-Minkowski problem in hyperbolic space

被引:1
作者
Li, Haizhong [1 ]
Wan, Yao [1 ]
Xu, Botong [2 ]
机构
[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
[2] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel
关键词
Discrete measure; h-convex polytope; Hyperbolic space; Horospherical p-Minkowski problem; FENCHEL TYPE INEQUALITIES; CONVEX-SETS; HYPERSURFACES; POLYTOPES;
D O I
10.1016/j.aim.2024.109851
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In [23], the first author and the third author introduced and studied the horospherical p-Minkowski problem for smooth horospherically convex domains in hyperbolic space. In this paper, we introduce and solve the discrete horospherical pMinkowski problem in hyperbolic space for all p is an element of (-infinity, +infinity) when the given measure is even on the unit sphere. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
引用
收藏
页数:31
相关论文
共 40 条
[1]  
Alexandroff A, 1942, CR ACAD SCI URSS, V35, P131
[2]   Volume preserving flow and Alexandrov-Fenchel type inequalities in hyperbolic space [J].
Andrews, Ben ;
Chen, Xuzhong ;
Wei, Yong .
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2021, 23 (07) :2467-2509
[3]  
Böröczky KJ, 2013, J AM MATH SOC, V26, P831
[4]   Total curvatures of convex hypersurfaces in hyperbolic space [J].
Borisenko, AA ;
Miquel, V .
ILLINOIS JOURNAL OF MATHEMATICS, 1999, 43 (01) :61-78
[5]  
Boroczky K.J.:., 2023, Harmonic_analysis_and_convexity, V9 of, P83
[6]   The planar Lp-Minkowski problem for 0 < p < 1 [J].
Boroczky, Karoly J. ;
Trinh, Hai T. .
ADVANCES IN APPLIED MATHEMATICS, 2017, 87 :58-81
[7]   On the Discrete Logarithmic Minkowski Problem [J].
Boroczky, Karoly J. ;
Hegedus, Pal ;
Zhu, Guangxian .
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2016, 2016 (06) :1807-1838
[8]   INTERIOR W2,P ESTIMATES FOR SOLUTIONS OF THE MONGE-AMPERE EQUATION [J].
CAFFARELLI, LA .
ANNALS OF MATHEMATICS, 1990, 131 (01) :135-150
[9]   LP Minkowski problem with not necessarily positive data [J].
Chen, WX .
ADVANCES IN MATHEMATICS, 2006, 201 (01) :77-89
[10]   REGULARITY OF SOLUTION OF N-DIMENSIONAL MINKOWSKI PROBLEM [J].
CHENG, SY ;
YAU, ST .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1976, 29 (05) :495-516