%0 Journal Article %T Some Isoperimetric Inequalities and Eigenvalue Estimates in Weighted Manifolds %A Marcio Batista %A Marcos P. Cavalcante %A Juncheol Pyo %J Mathematics %D 2013 %I arXiv %X In this paper we prove general inequalities involving the weighted mean curvature of compact submanifolds immersed in weighted manifolds. As a consequence we obtain a relative linear isoperimetric inequality for such submanifolds. We also prove an extrinsic upper bound to the first non zero eigenvalue of the drift Laplacian on closed submanifolds of weighted manifolds. %U http://arxiv.org/abs/1306.4874v3