A fully nonlinear locally constrained curvature flow for capillary hypersurface
arXiv:2408.13815 · doi:10.1007/s10455-024-09983-8
Abstract
In this article, we study a locally constrained fully nonlinear curvature flow for convex capillary hypersurfaces in half-space. We prove that the flow preserves the convexity, exists for all time, and converges smoothly to a spherical cap. This can be viewed as the fully nonlinear counterpart of the result in \cite{MWW}. As a byproduct, a high-order capillary isoperimetric ratio (1.6) evolves monotonically along this flow, which yields a class of the Alexandrov-Fenchel inequalities.
arXiv comment16 pages
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