A mean curvature type flow with capillary boundary in a unit ball
Guofang Wang, Liangjun Weng
Abstract
Abstract In this paper, we study a mean curvature type flow with capillary boundary in the unit ball. Our flow preserves the volume of the bounded domain enclosed by the hypersurface, and monotonically decreases an energy functional E . We show that it has the longtime existence and subconverges to spherical caps. As an application, we solve an isoperimetric problem for hypersurfaces with capillary boundary.
Topics & Concepts
MathematicsIsoperimetric inequalityMean curvature flowMean curvatureUnit sphereHypersurfaceCapillary actionCurvatureBall (mathematics)Bounded functionMathematical analysisBoundary (topology)Willmore energyGeometryPhysicsThermodynamicsGeometric Analysis and Curvature FlowsGeometry and complex manifoldsAnalytic and geometric function theory