Alexandrov–Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary
Guofang Wang, Liangjun Weng, Chao Xia
Abstract
Abstract In 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.
Topics & Concepts
MathematicsIsoperimetric inequalityRegular polygonCapillary actionCurvatureBoundary (topology)Mathematical analysisFlow (mathematics)Space (punctuation)Mean curvature flowMean curvaturePure mathematicsGeometryPhysicsComputer scienceThermodynamicsOperating systemGeometric Analysis and Curvature FlowsPoint processes and geometric inequalitiesGeometry and complex manifolds