Some Isoperimetric Inequalities and Eigenvalue Estimates in Weighted Manifolds

摘要

In this paper we prove general inequalities involving the weighted meancurvature of compact submanifolds immersed in weighted manifolds. As aconsequence we obtain a relative linear isoperimetric inequality for suchsubmanifolds. We also prove an extrinsic upper bound to the first non zeroeigenvalue of the drift Laplacian on closed submanifolds of weighted manifolds.