Year
Month
(Peer-Reviewed) The anisotropic p-capacity and the anisotropic Minkowski inequality
Chao Xia 夏超, Jiabin Yin 尹佳斌
School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
中国 厦门 厦门大学数学科学学院
Abstract

In this paper, we prove a sharp anisotropic Lᵖ Minkowski inequality involving the total Lᵖ anisotropic mean curvature and the anisotropic p-capacity for any bounded domains with smooth boundary in Rⁿ. As consequences, we obtain an anisotropic Willmore inequality, a sharp anisotropic Minkowski inequality for outward F-minimising sets and a sharp volumetric anisotropic Minkowski inequality. For the proof, we utilize a nonlinear potential theoretic approach which has been recently developed by Agostiniani et al. (2019).
The anisotropic p-capacity and the anisotropic Minkowski inequality_1
The anisotropic p-capacity and the anisotropic Minkowski inequality_2
The anisotropic p-capacity and the anisotropic Minkowski inequality_3
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