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This is a Quantitative Study study.

October 15, 2025Open Access

Inverse curvature flows for capillary hypersurfaces in the unit ball

Key Points

Establishes the existence and convergence of inverse curvature flows for strictly convex hypersurfaces.
Derives a family of Alexandrov Fenchel inequalities applicable to weakly convex hypersurfaces.
Focuses on capillary hypersurfaces within the framework of the unit Euclidean ball.
Implications for geometric analysis are significant, particularly of free boundary conditions.

Abstract

In this paper, we study inverse curvature flows for strictly convex, capillary hypersurfaces in the unit Euclidean ball. We establish the existence and convergence results for a class of such flows. As an application, we derive a family of Alexandrov Fenchel inequalities for weakly convex hypersurfaces with free boundary.

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Cite This Study

Pan et al. (Wed,) studied this question.

synapsesocial.com/papers/68ef858cc6a308ba06355510 https://doi.org/https://doi.org/10.48550/arxiv.2507.12097

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