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A constrained mean curvature flow and Alexandrov-Fenchel inequalities by Mei, Xinqun; Wang, Guofang; Weng, Liangjun is a scholarly article available to read on EtoBox.

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In this article, we study a locally constrained mean curvature flow for star-shaped hypersurfaces with capillary boundary in the half-space. We prove its long-time existence and the global convergence to a spherical cap. Furthermore, the capillary quermassintegrals defined in \cite{WWX2022} evolve monotonically along the flow, and hence we establish a class of new Alexandrov-Fenchel inequalities for convex hypersurfaces with capillary boundary in the half-space.

Author

Mei, Xinqun; Wang, Guofang; Weng, Liangjun

Published

2022

Language

EN