Quantitative stability of Sobolev Inequalities on Closed Riemannian Manifolds.

par Davide Parise ((San Diego - University of California))

mardi 17 déc. 2024, 14:00 → 15:00 Europe/Paris

Fokko (ICJ)

 I will present a recent joint work with Francesco Nobili in which we prove quantitative stability results for different classes of Sobolev inequalities on closed Riemannian manifolds. In a nutshell, we will see that up to constants depending on the manifold, a function that nearly saturates a critical Sobolev inequality is quantitatively W^{1, 2}-close to a non-empty set of extremal functions, provided that the corresponding optimal

Sobolev constants satisfy suitable strict bounds. We will also discuss degenerate phenomena in our quantitative controls, the subcritical case, and we will conclude with some open problems and remarks beyond the setting of Sobolev functions (e.g. Yang-Mills connections).