A Heintze-Karcher-type inequality for hypersurfaces with capillary boundary

DOI10.1007/s12220-023-01230-zOpenAlexW4221139302MaRDI QIDQ2698529

Xiaohan Jia, Chao Xia, Xuwen Zhang

Publication date: 24 April 2023

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.06931

zbMATH Keywords

mixed boundary value problemAlexandrov's theoremReilly's formulacapillary hypersurfaceHeintze-Karcher inequality

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Rigidity results (53C24) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

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Cites Work

• Unnamed Item
• Overdetermined problems and constant mean curvature surfaces in cones
• Optimal Hölder regularity for mixed boundary value problems
• Mixed boundary value problems for elliptic and parabolic differential equations of second order
• Compact hypersurfaces with constant higher order mean curvatures
• The symmetry of sessile and pendent drops
• On stability of capillary surfaces in a ball
• Capillary surfaces with free boundary in a wedge
• A partially overdetermined problem in a half ball
• Uniqueness of stable capillary hypersurfaces in a ball
• An integral formula and its applications on sub-static manifolds
• Capillary surfaces in a convex cone
• A symmetry problem in potential theory
• Stable capillary hypersurfaces in a half-space or a slab
• Sets of Finite Perimeter and Geometric Variational Problems
• A Generalization of Reilly's Formula and its Applications to a New Heintze–Karcher Type Inequality
• A general comparison theorem with applications to volume estimates for submanifolds
• A variational problem for constant mean curvature surfaces with free boundary.
• Uniqueness theorems for surfaces in the large. I, II, III, IV, V