General affine surface areas

被引：166
作者：
Ludwig, Monika [1 ]
机构：
[1] NYU, Polytech Inst, Dept Math, MetroTech Ctr 6, Brooklyn, NY 11201 USA
来源：
ADVANCES IN MATHEMATICS | 2010年 / 224卷 / 06期
关键词：
Aftine surface area; Centro-aftine surface area; Valuation; P SOBOLEV INEQUALITIES; MINKOWSKI-FIREY THEORY; ISOPERIMETRIC-INEQUALITIES; CONVEX HYPERSURFACES; STEPWISE APPROXIMATION; L-0-MINKOWSKI PROBLEM; VALUED VALUATIONS; BODIES; SEMICONTINUITY; REGULARITY;
D O I：
10.1016/j.aim.2010.02.004
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Two families of general affine surface areas are introduced. Basic properties and affine isoperimetric inequalities for these new affine surface areas as well as for L phi affine surface areas are established. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：2346 / 2360
页数：15
相关论文
共 54 条
[1]  
Andrews B, 1999, J REINE ANGEW MATH, V506, P43
[2]  
Andrews B, 1996, J DIFFER GEOM, V43, P207
[3]  
[Anonymous], 2007, GRUNDLEHREN MATH WIS
[4]   Sylvester's question:: The probability that n points are in convex position [J].
Bárány, I .
ANNALS OF PROBABILITY, 1999, 27 (04) :2020-2034
[5]  
Barany I, 1997, J REINE ANGEW MATH, V484, P71
[6]  
BLASCHKE W, 1923, DIFFERENTIALGEOMETRI, VII
[7]   The Lp-Busemann-Petty centroid inequality [J].
Campi, S ;
Gronchi, P .
ADVANCES IN MATHEMATICS, 2002, 167 (01) :128-141
[8]   The Lp-Minkowski problem and the Minkowski problem in centroaffine geometry [J].
Chou, Kai-Seng ;
Wang, Xu-Jia .
ADVANCES IN MATHEMATICS, 2006, 205 (01) :33-83
[9]   Affine Moser-Trudinger and Morrey-Sobolev inequalities [J].
Cianchi, Andrea ;
Lutwak, Erwin ;
Yang, Deane ;
Zhang, Gaoyong .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2009, 36 (03) :419-436
[10]  
Federer H., 1969, Geometric Measure Theory. Classics in Mathematics
123456