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

[21] LP ESTIMATES FOR INTEGRAL TRANSFORMS
WALSH, T
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 155 (01) : 195 - &
[22] ON THE FRACTIONAL INTEGRAL OF WEYL IN LP
MARTINEZ, C
MARTINEZ, MD
SANZ, M
MATHEMATISCHE ZEITSCHRIFT, 1994, 215 (02) : 209 - 221
[23] The Lp-curvature images of convex bodies and Lp-projection bodies
Songjun Lv
Gangsong Leng
Proceedings Mathematical Sciences, 2008, 118 : 413 - 424
[24] The Lp-curvature images of convex bodies and Lp-projection bodies
Lv, Songjun
Leng, Gangsong
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2008, 118 (03): : 413 - 424
[25] Ricci curvature and Lp-convergence
Honda, Shouhei
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2015, 705 : 85 - 154
[26] Effective Lp pinching for the concircular curvature
Hebey, Emmanuel
Vaugon, Michel
Journal of Geometric Analysis, 1996, 6 (04): : 531 - 553
[27] Effective Lp pinching for the concircular curvature
J Geom Anal, 4 (531-553):
[28] A CLASS OF INVERSE CURVATURE FLOWS AND LP DUAL CHRISTOFFEL-MINKOWSKI PROBLEM
Ding, Shanwei
LI, Guanghan
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, 376 (01) : 697 - 752
[29] A curvature flow to the Lp Minkowski-type problem of q-capacity
Liu, Xinying
Sheng, Weimin
ADVANCED NONLINEAR STUDIES, 2023, 23 (01)
[30] A priori bounds and existence of smooth solutions to a Lp Aleksandrov problem for Codazzi tensor with log-convex measure
Chen, Zhengmao
ELECTRONIC RESEARCH ARCHIVE, 2022, 31 (02): : 840 - 859

← 1 2 3 4 5 →