Some Isoperimetric Inequalities and Eigenvalue Estimates in Weighted Manifolds

2013/06/20 by Márcio Batista, Marcos P. Cavalcante, Batista, Marcio +3 · 2 citations
Mathematics · #53C42 #58J50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1306.4874

openalex publication_date 2013/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Integral Formulas for Differential Forms on Weighted Manifolds and Applications
• First eigenvalue estimates on complete balanced Hermitian manifolds

Related

• Sobolev and isoperimetric inequalities for submanifolds in weighted\n ambient spaces
• Eigenvalues of Laplacian and multi-way isoperimetric constants on\n weighted Riemannian manifolds
• Weighted isoperimetric inequalities in warped product manifolds
• Intrinsic and extrinsic comparison results for isoperimetric quotients and capacities in weighted manifolds
• Eigenvalue estimates and applications on weighted manifolds