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math.AP2023
Faber-Krahn inequalities, the Alt-Caffarelli-Friedman formula, and Carleson's conjecture in higher dimensions
Ian Fleschler, Xavier Tolsa, Michele Villa
The main aim of this article is to prove quantitative spectral inequalities for the Laplacian with Dirichlet boundary conditions. More specifically, we prove sharp quantitative sta…
math.AP2019★ 8 cited
Quantitative Comparisons of Multiscale Geometric Properties
Jonas Azzam, Michele Villa
We generalize some characterizations of uniformly rectifiable (UR) sets to sets whose Hausdorff content is lower regular (and in particular, do not need to be Ahlfors regular). For…