A Minkowski-type inequality for capillary hypersurfaces in a half-space

DOI10.1016/J.JFA.2024.110496arXiv2209.13516OpenAlexW4396696436MaRDI QIDQ6412129

Guofang Wang, Chao Xia, Liangjun Weng

Publication date: 27 September 2022

Abstract: This paper is a continuation of our previous work cite{WWX2022} concerning Alexandrov-Fenchel inequalities for capillary hypersurfaces in the half-space. We obtain, in this paper, a new class of the Alexandrov-Fenchel inequalities for hypersurface with capillary boundary in the half-space under mild assumptions, the hypersurfaces are $k$-convex and star-shaped, which is optimal compared to the counterpart result of the closed case by Guan-Li cite{GL09}. In particular, we give an affirmative answer to the question in cite[Conjecture 1.5]{WWX2022} provided $hetain(0,fracpi2]$.

Full work available at URL: https://doi.org/10.1016/j.jfa.2024.110496

Mathematics Subject Classification ID

Rigidity results (53C24) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Quasilinear parabolic equations with mean curvature operator (35K93) Flows related to mean curvature (53E10)

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