Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$

Abstract

We prove stability for the affine Sobolev inequality for exponents $p\ge 2$ with best possible norm and best possible stability exponent. We also show a corresponding result for critical points of the functional in the absence of bubbling. An important ingredient in our proof is the classification of positive energy solutions to the critical affine $p$-Laplace equation.

76 pages