Calculus of Variations and Geometric Measure Theory

S. Nardulli - A. Muñoz Flores

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

created by nardulli on 12 Apr 2014
modified on 25 Jan 2016


Submitted Paper

Inserted: 12 apr 2014
Last Updated: 25 jan 2016

Year: 2014

13 pages.


For a complete noncompact connected Riemannian manifold with bounded geometry $M^n$, we prove that the isoperimetric profile function $I_{M^n}$ 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.