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Geometria Diferencial

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

Terça-feira, 3 de abril de 2018, 15:30
Sala 236.

For a complete noncompact connected Riemannian manifold with bounded geometry $M^n$, we prove that the isoperimetric profile function $I_{M^n}$ is a locally $(1-\frac{1}{n})$-Hölder continuous function so in particular it is continuous. Here for bounded geometry, we mean that M has 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 isoperimetric profile function in complete Riemannian manifolds which is based on a lemma having its own interest about the approximation of finite perimeter sets with finite volume by open bounded with smooth boundary ones of the same volume. This is a joint work with Stefano Nardulli.