Continuity and differentiability properties of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry

2014/04/11 by Flores, Abraham Muñoz, Nardulli, Stefano
#49Q05 #49Q20 #53A10 #58E99 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1404.3245

Abstract

For a complete noncompact connected Riemannian manifold with bounded geometry Mⁿ, we prove that the isoperimetric profile function I_Mⁿ is continuous. Here for bounded geometry we mean that M have Ricci curvature bounded below and volume of balls of radius 1, uniformly bounded below with respect to its centers. Then under an extra hypothesis on the geometry of M, we apply this result to prove some differentiability property of I_M and a differential inequality satisfied by I_M, extending in this way well known results for compact manifolds, to this class of noncompact complete Riemannian manifolds with bounded geometry.

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