Local Hölder continuity of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry

@article{Flores2016LocalHC,
  title={Local H{\"o}lder continuity of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry},
  author={Abraham Enrique Mu{\~n}oz Flores and S. Nardulli},
  journal={Geometriae Dedicata},
  year={2016},
  pages={1-12}
}
For a complete noncompact connected Riemannian manifold with bounded geometry $$M^n$$Mn, we prove that the isoperimetric profile function $$I_{M^n}$$IMn is a locally $$(1-\frac{1}{n})$$(1-1n)-Hölder continuous function and so in particular it 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. We prove also the equivalence of the weak and strong formulation of the… Expand
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