Published Paper

Inserted: 10 dec 2024
Last Updated: 21 aug 2025

Journal: Indag. Math.
Year: 2024
Doi: https://doi.org/10.1016/j.indag.2025.07.004

Abstract:

We review recent results regarding the problem of the stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds. We shall describe techniques and methods from smooth and non-smooth geometry, the fruitful combination of which revealed particularly effective. Furthermore, we present a self-contained overview of the proof of the stability of the Sobolev inequality on manifolds with non-negative Ricci curvature and Euclidean volume growth, adopting a direct strategy tailored to this setting. Finally, we discuss related stability results and present some open problems.