From the 1 of 9 linked papers with an AI index.
9 papers
Mean curvature and sharp Willmore inequalities in metric spaces
Nicola Gigli, Ivan Yuri Violo
The paper defines a notion of mean curvature for level sets of Sobolev functions in non‑smooth metric spaces with Ricci curvature bounded below, introduces a Willmore functional, a…
Quantitative stability in distribution for the Sobolev inequality under curvature dimension condition
Max Fathi, Ivan Yuri Violo
The goal of this note is to investigate quantitative stability properties of the critical Sobolev inequality in metric measure spaces. Assuming that the optimal c…
On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 2
Katrin Fässler, Ivan Yuri Violo
We characterize uniform -rectifiability in Euclidean spaces in terms of a Carleson-type geometric lemma for a new notion of flatness coefficients, which we call -numbers. Th…
Generalized existence of extremizers for the sharp -Sobolev inequality on Riemannian manifolds with nonnegative curvature
Francesco Nobili, Ivan Yuri Violo
We study the generalized existence of extremizers for the sharp -Sobolev inequality on noncompact Riemannian manifolds in connection with nonnegative curvature and Euclidean vol…
Regularity for quasilinear elliptic equations in metric measure spaces
Simon Schulz, Ivan Yuri Violo
In the present article we prove second-order and Lipschitz regularity for quasilinear elliptic equations in metric spaces endowed with a lower bound on the Ricci curvature. The est…
Fine Pólya-SzegŠrearrangement inequalities in metric spaces and applications
Francesco Nobili, Ivan Yuri Violo
We study fine Pólya-SzegÅ rearrangement inequalities into weighted intervals for Sobolev functions and functions of bounded variation defined on metric measure spaces supporting…