At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …

This book is about differentiation of functions. It is divided into two parts, which can be used
as different textbooks, one for an advanced undergraduate course in functions of one …

A sharp quantitative version of the anisotropic isoperimetric inequality is established,
corresponding to a stability estimate for the Wulff shape of a given surface tension energy …

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 …

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 …

In this paper, we are concerned with the stability problem for endpoint conformally invariant
cases of the Sobolev inequality on the sphere S n. Namely, we will establish the stability for …

The quantitative isoperimetric inequality and related topics | Bulletin of Mathematical Sciences
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We show that the fractional Sobolev inequality for the embedding H̊s/2 (ℝN)↪ L2N/(N–
s)(ℝN), s∈(0, N) can be sharpened by adding a remainder term proportional to the distance …