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, Jiabin Yin
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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