Cari tutti,
sono lieta di annunciarvi il seminario di Francesco Nobili (che ha da poco iniziato un PostDoc presso il nostro Dipartimento!)
mercoledì 13 dicembre, ore 14:15, aula Seminari.
Attenzione: l'orario è un po' strano per evitare di sovrapporci con il colloquio di dipartimento.
Titolo: Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds.
Abstract:
The problem of stability of the Sobolev inequality in the Euclidean space asks how a function achieving almost equality is close to the family of extremals. This question has received a lot of attention in recent years and is now well understood.
On the other hand, in the setting of Riemannian manifolds, very few is known except in specific cases. In this seminar, we show that almost extremal functions for the sharp Sobolev inequality on Riemannian manifolds with non-negative Ricci curvature and Euclidean volume growth are close to radial profiles of Euclidean extremals. An analogous result is established under positive Ricci lower bounds in comparison with radial profiles of extremals of the round sphere. Our arguments rely on rigidity properties of Sobolev inequalities and a generalized version of Lions’ concentration compactness in non-smooth settings. Based on joint works with I. Y. Violo.
https://www.dm.unipi.it/seminario/?id=6576dc2ed0301798be4ede4c