On the mean curvature type flow for convex capillary hypersurfaces in the ball

In this paper, we study the mean curvature type flow for hypersurfaces in the unit Euclidean ball with capillary boundary, which was introduced by Wang and Xia (Commun Anal Geom, 2019) and Wang and Weng (Calc Var Partial Differ Equ 59(5):149–174, 2020). We show that if the initial hypersurface is st...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2023-09, Vol.62 (7), Article 209
Main Authors: Hu, Yingxiang, Wei, Yong, Yang, Bo, Zhou, Tailong
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Capillary flow
Control
Curvature
Hyperspaces
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Spherical caps
Systems Theory
Theoretical
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Summary:In this paper, we study the mean curvature type flow for hypersurfaces in the unit Euclidean ball with capillary boundary, which was introduced by Wang and Xia (Commun Anal Geom, 2019) and Wang and Weng (Calc Var Partial Differ Equ 59(5):149–174, 2020). We show that if the initial hypersurface is strictly convex, then the solution of this flow is strictly convex for t > 0 , exists for all positive time and converges smoothly to a spherical cap. As an application, we prove a family of new Alexandrov–Fenchel inequalities for convex hypersurfaces in the unit Euclidean ball with capillary boundary.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-023-02554-y