THE Lp-ALEKSANDROV PROBLEM FOR Lp-INTEGRAL CURVATURE

被引：3

作者：

Huang, Yong ^{[1
]}

Lutwak, Erwin ^{[2
]}

Yang, Deane ^{[2
]}

Zhang, Gaoyong ^{[2
]}

机构：

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

[2] NYU, Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA

来源：

JOURNAL OF DIFFERENTIAL GEOMETRY | 2018年 / 110卷 / 01期

关键词：

Curvature measure; surface area measure; integral curvature; L-p-integral curvature; Minkowski problem; Aleksandrov problem; L-p-Minkowski problem; L-p-Aleksandrov problem; MINKOWSKI PROBLEM; SYMMETRIC-SOLUTIONS; GAUSS CURVATURE; HYPERSURFACES; CLASSIFICATION; REGULARITY; EQUATIONS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that within the L-p-Brunn-Minkowski theory that Aleksandrov's integral curvature has a natural L-p extension, for all real p. This raises the question of finding necessary and sufficient conditions on a given measure in order for it to be the L-p-integral curvature of a convex body. This problem is solved for positive p and is answered for negative p provided the given measure is even.

引用

页码：1 / 29

页数：29

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