Volumes and Limits of Manifolds with Ricci Curvature and Mean Curvature\n Bounds

2014/04/02 by Raquel Perales, Perales, Raquel
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1404.0560

Abstract

We prove a laplacian comparison theorem in the barrier sense for the function\ndistance to the boundary of Riemannian manifolds with nonnegative Ricci\ncurvature, area and mean curvature of the boundary bounded above. As an\napplication we get volume estimates, different to the ones obtained by\nHeintz-Karcher, and area estimates. With those estimates we prove\nSormani-Wenger Intrinsic Flat (SWIF) compactness theorems for sequences of such\nmanifolds with uniform bounds.\n

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