Differentiability of the isoperimetric profile and topology of analytic Riemannian manifolds

Abstract We show that smooth isoperimetric profiles are exceptional for real analytic Riemannian manifolds. For instance, under some extra assumptions, this can happen only on topological spheres. To cite this article: R. Grimaldi et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).

Differentiability properties of the isoperimetric profile and topology of analytic Riemannian manifolds.

Abstract: We show that smooth isoperimetric profiles are exceptional for real analytic Riemannian manifolds. For instance, under some extra assumptions, this can happen only on topological spheres

Semianalyticity of isoperimetric profiles

It is shown that, in dimensions $<8$, isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic.

The isoperimetric profile of a smooth Riemannian manifold for small volumes.