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math.DG2022
Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds
Francesco Nobili, Ivan Yuri Violo
We study the qualitative stability of two classes of Sobolev inequalities on Riemannian manifolds. In the case of positive Ricci curvature, we prove that an almost extremal functio…
math.DG2021
Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds
Francesco Nobili, Ivan Yuri Violo
We prove that if is a closed -dimensional Riemannian manifold, , with and for which the optimal constant in the critical Sobolev inequality equal…