摘要：

Isoperimetric inequality is one of the oldest problems in mathematics, which relates with convex geometry, differential geometry and geometric PDEs, etc. Recently, the isoperimetric type inequalities in hyperbolic space have been widely investigated by using the hypersurface curvature flows, including the inverse curvature flows, quermassintegral preserving curvature flows, contracting curvature flows, and locally constrained curvature flows. In this talk, I will survey the recent progress in this direction, which is based on my joint works with my  coauthors.