期刊
SCIENCE CHINA-MATHEMATICS
卷 65, 期 3, 页码 559-582出版社
SCIENCE PRESS
DOI: 10.1007/s11425-021-1884-1
关键词
Minkowski inequality; anisotropic mean curvature; anisotropic p-Laplacian; nonlinear potential theory; p-capacity
资金
- National Natural Science Foundation of China [11871406]
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 Double-struck capital 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 by Agostiniani et al. (2019).
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 Double-struck capital 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 by Agostiniani et al. (2019).
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