A fully nonlinear locally constrained curvature flow for capillary hypersurface

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 Mei et al. (Int Math Res Not IMRN 1:152–174, 2024). 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.