Sharp bounds for the anisotropic p-capacity of Euclidean compact sets

被引：2
|
作者：
Li, Ruixuan [1 ]
Xiong, Changwei [2 ]
机构：
[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
[2] Sichuan Univ, Coll Math, Chengdu 610065, Sichuan, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2022年 / 317卷
关键词：
Anisotropic p-capacity; Inverse anisotropic mean curvature flow; Anisotropic Hawking mass; MEAN-CURVATURE FLOW; HYPERSURFACES; MANIFOLDS;
D O I：
10.1016/j.jde.2022.02.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove various sharp bounds for the anisotropic p-capacity CapF,p(K) (1 < p < n) of compact sets K in the Euclidean space Rn (n >= 2). Our results are mainly the anisotropic generalizations of some isotropic 2017] and [Xiao, Adv. Geom. 2017]. Key ingredients in the proofs include the inverse anisotropic mean curvature flow (IAMCF), the anisotropic Hawking mass and its monotonicity property along IAMCF for certain surfaces, and the anisotropic isocapacitary inequality. (c) 2022 Elsevier Inc. All rights reserved.
引用
收藏
页码：196 / 224
页数：29
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