3 papers
math.AP2025
An overview of regularity results for the Laplacian and -Laplacian in metric spaces
Ivan Yuri Violo
We review some regularity results for the Laplacian and -Laplacian in metric measure spaces. The focus is mainly on interior Hölder, Lipschitz and second-regularity estimates an…
math.MG2024
Notes on the Cheeger and Colding version of the Reifenberg theorem for metric spaces
Nicola Gigli, Ivan Yuri Violo
The classical Reifenberg's theorem says that a set which is sufficiently well approximated by planes uniformly at all scales is a topological Hölder manifold. Remarkably, this gene…
math.MG2023
Ricci curvature bounded below and uniform rectifiability
Matthew Hyde, Michele Villa, Ivan Yuri Violo
We prove that Ahlfors-regular RCD spaces are uniformly rectifiable. The same is shown for Ahlfors regular boundaries of non-collapsed RCD spaces. As an application we deduce a type…