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

共 50 条

[41] The Lp chord Minkowski problem
Xi, Dongmeng
Yang, Deane
Zhang, Gaoyong
Zhao, Yiming
ADVANCED NONLINEAR STUDIES, 2023, 23 (01)
[42] On the Lp Minkowski Problem for Polytopes
Daniel Hug
Erwin Lutwak
Deane Yang
Gaoyong Zhang
Discrete & Computational Geometry, 2005, 33 : 699 - 715
[43] On the Lp Minkowski problem for polytopes
Hug, D
Lutwak, E
Yang, D
Zhang, G
DISCRETE & COMPUTATIONAL GEOMETRY, 2005, 33 (04) : 699 - 715
[44] On the regularity of the Lp Minkowski problem
Huang, Yong
Lu, QiuPing
ADVANCES IN APPLIED MATHEMATICS, 2013, 50 (02) : 268 - 280
[45] The Lp Gauss image problem
Wu, Chuanxi
Wu, Di
Xiang, Ni
GEOMETRIAE DEDICATA, 2022, 216 (06)
[46] The strip problem for Lp functions
Lawrence, Mark G.
INTERNATIONAL JOURNAL OF MATHEMATICS, 2015, 26 (11)
[47] Stability in the Lp Shephard problem
Hu, Junfang
INDAGATIONES MATHEMATICAE-NEW SERIES, 2014, 25 (03): : 454 - 467
[48] On the Lp-Minkowski problem
Lutwak, E
Yang, D
Zhang, GY
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (11) : 4359 - 4370
[49] On the Lp Gaussian Minkowski problem
Feng, Yibin
Hu, Shengnan
Xu, Lei
JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 363 : 350 - 390
[50] LP SOLUTION OF A MANUFACTURING PROBLEM
MASON, EE
OPERATIONS RESEARCH, 1965, S 13 : B151 - &

← 1 2 3 4 5 →