The planar Lp-Minkowski problem for 0 < p < 1

被引:40
作者
Boroczky, Karoly J. [1 ,2 ]
Trinh, Hai T. [2 ]
机构
[1] Hungarian Acad Sci, Alfred Renyi Inst Math, Realtanoda U 13-15, H-1053 Budapest, Hungary
[2] Cent European Univ, Dept Math, Nador U 9, H-1051 Budapest, Hungary
关键词
L-p Minkowski problem; Monge-Ampere equation; SURFACE MEASURE; REGULARITY; FLOW; CLASSIFICATION; INEQUALITY; CURVATURE; GEOMETRY; SPHERE;
D O I
10.1016/j.aam.2016.12.007
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The planar L-p Minkowski problem is solved for p epsilon (0,1). (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码:58 / 81
页数:24
相关论文
共 67 条
[1]  
Alexandroff A, 1942, CR ACAD SCI URSS, V35, P131
[2]  
Andrews B, 2003, J AM MATH SOC, V16, P443
[3]   Gauss curvature flow: the fate of the rolling stones [J].
Andrews, B .
INVENTIONES MATHEMATICAE, 1999, 138 (01) :151-161
[4]  
[Anonymous], 2007, GRUNDLEHREN MATH WIS
[5]   A probabilistic approach to the geometry of the lnp-ball [J].
Barthe, F ;
Guédon, O ;
Mendelson, S ;
Naor, A .
ANNALS OF PROBABILITY, 2005, 33 (02) :480-513
[6]   Cone-volume measure of general centered convex bodies [J].
Boeroeczky, Karoly J. ;
Henk, Martin .
ADVANCES IN MATHEMATICS, 2016, 286 :703-721
[7]  
Böröczky KJ, 2015, J DIFFER GEOM, V99, P407
[8]  
Böröczky KJ, 2013, J AM MATH SOC, V26, P831
[9]   The log-Brunn-Minkowski inequality [J].
Boeroeczky, Karoly J. ;
Lutwak, Erwin ;
Yang, Deane ;
Zhang, Gaoyong .
ADVANCES IN MATHEMATICS, 2012, 231 (3-4) :1974-1997
[10]   INTERIOR W2,P ESTIMATES FOR SOLUTIONS OF THE MONGE-AMPERE EQUATION [J].
CAFFARELLI, LA .
ANNALS OF MATHEMATICS, 1990, 131 (01) :135-150