We obtain a sharp quantitative isoperimetric inequality for nonlocal s-perimeters, uniform
with respect to s bounded away from 0. This allows us to address local and global minimality …

We prove that if (X, d, m)(X, d, m) is a metric measure space with m (X)= 1 m (X)= 1 having
(in a synthetic sense) Ricci curvature bounded from below by K> 0 K> 0 and dimension …

We discuss the local minimality of certain configurations for a nonlocal isoperimetric problem
used to model microphase separation in diblock copolymer melts. We show that critical …

Sharp gradient stability for the Sobolev inequality Page 1 SHARP GRADIENT STABILITY FOR
THE SOBOLEV INEQUALITY ALESSIO FIGALLI and YI RU-YA ZHANG Abstract We prove a …

Abstract The classical Faber–Krahn inequality asserts that balls (uniquely) minimize the first
eigenvalue of the Dirichlet Laplacian among sets with given volume. In this article we prove …

We prove a sharp quantitative version for the stability of the Sobolev inequality with explicit
constants. Moreover, the constants have the correct behavior in the limit of large dimensions …

We show that on S1. 1= pd 2/Sd1. 1/the conformally invariant Sobolev inequality holds with
a remainder term that is the fourth power of the distance to the optimizers. The fourth power …

Mathematical Analysis. – An overview on extremals and critical points of the Sobolev inequality
in convex cones, by Alberto Ro Page 1 Rend. Lincei Mat. Appl. 33 (2022), 967–995 DOI …

We consider a nonlocal isoperimetric problem defined in the whole space R^N, whose
nonlocal part is given by a Riesz potential with exponent α∈(0,N-1). We show that critical …

The quantitative isoperimetric inequality and related topics | Bulletin of Mathematical Sciences
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