No abstract

In this paper, we prove a class of weighted isoperimetric inequalities for bounded domains in hyperbolic space by using the isoperimetric inequality with logconvex density in Euclidean space. As a consequence, we remove the horo-convex assumption of domains in a weighted isoperimetric inequality proved by Scheuer-Xia. Furthermore, we prove weighted isoperimetric inequalities for star-shaped domains in warped product manifolds. Particularly, we obtain a weighted isoperimetric inequality for star-shaped hypersurfaces lying outside a certain radial coordinate slice in the antide Sitter-Schwarzschild manifold.

Special Issue on Differential Geometry . ARTICLES . A class of inverse mean curvature type flows in the anti-de Sitter-Schwarzschild manifold