论文标题
各向异性$ P $ - 容量和各向异性Minkowski不平等
Anisotropic $p$-capacity and anisotropic Minkowski inequality
论文作者
论文摘要
在本文中，我们证明了尖锐的各向异性$ l^p $ minkowski不平等，涉及总$ l^p $各向异性平均曲率和各向异性$ p $ p $ - 容量，对于任何具有$ \ mathbb {r}^n $ $ \ mathbb {r}^n $的有界边界的有界域而言。结果，我们获得了各向异性的威尔莫尔不平等，尖锐的各向异性Minkowski不平等，用于外向$ f $ iniminimising套件和急剧的体积各向异性Minkowski不平等。为了证明，我们利用了最近在\ cite {afm1}中开发的非线性潜在理论方法。
In this paper, we prove a sharp anisotropic $L^p$ Minkowski inequality involving the total $L^p$ anisotropic mean curvature and the anisotropic $p$-capacity, for any bounded domains with smooth boundary in $\mathbb{R}^n$. 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 in \cite{AFM1}.
