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.
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页码：1 / 29
页数：29
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