The anisotropic p-capacity and the anisotropic Minkowski inequality
各向异性 p 容量和各向异性 Minkowski 不等式
등방성 p-용량 및 이방성 Minkowski 부등식
La capacidad p anisotrópica y la desigualdad anisotrópica de Minkowski
La p-capacité anisotrope et l'inégalité de Minkowski anisotrope
Анизотропная p-емкость и анизотропное неравенство Минковского
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
Science China Mathematics, 15 October 2021

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).
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