Curvature flows of hypersurfaces and geometric inequalities
摘要：Curvature flows of hypersurfaces are characterized by a family of hypersurfaces evolving in an ambient manifold with velocity determined by their extrinsic curvatures. The equations that arise are nonlinear parabolic differential equations. The curvature flows of hypersurfaces have many applications including the proof of some sharp geometric inequalities. In this talk, I will describe some recent work on this topic, with focus on the applications of curvature flows in the proof of isoperimetric type inequalities in Euclidean space and in hyperbolic space.