Abstract
AbstractIn this paper, we first introduce quermassintegrals for capillary hypersurfaces in the half-space. Then we solve the related isoperimetric type problems for the convex capillary hypersurfaces and obtain the corresponding Alexandrov–Fenchel inequalities. In order to prove these results, we construct a new locally constrained curvature flow and prove that the flow converges globally to a spherical cap.
Funder
Postdoctoral Research Foundation of China
Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Reference61 articles.
1. Agostiniani, V., Fogagnolo, M., Mazzieri, L.: Minkowski inequalities via nonlinear potential theory. Arch. Rat. Mech. Anal. 244(1), 51–85 (2022)
2. Ainouz, A., Souam, R.: Stable capillary hypersurfaces in a half-space or a slab. Indiana Univ. Math. J. 65(3), 813–831 (2016)
3. Alexandrov, A.D.: Zur Theorie der gemischten Volumina von konvexen Körpern, II. Neue Ungleichungen zwischen den gemischten Volumina und ihre Anwendungen. Mat. Sb. (N.S.) 2, 1205–1238 (1937) (in Russian)
4. Alexandrov, A.D.: Zur Theorie der gemischten Volumina von konvexen Körpern, III. Die Erweiterung zweeier Lehrsatze Minkowskis über die konvexen Polyeder auf beliebige konvexe Flachen. Mat. Sb. (N.S.) 3, 27–46 (1938) (in Russian)
5. Altschuler, S.J., Wu, L.F.: Translating surfaces of the non-parametric mean curvature flow with prescribed contact angle. Calc. Var. Partial Differ. Equ. 2(1), 101–111 (1994)
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