5 papers
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…
A first-order condition for the independence on of weak gradients
Nicola Gigli, Francesco Nobili
It is well known that on arbitrary metric measure spaces, the notion of minimal -weak upper gradient may depend on . In this paper we investigate how a first-order condition…
On master test plans for the space of BV functions
Francesco Nobili, Enrico Pasqualetto, Timo Schultz
We prove that on an arbitrary metric measure space a countable collection of test plans is sufficient to recover all functions and their total variation measures. In the s…
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…
A differential perspective on Gradient Flows on -spaces and applications
Nicola Gigli, Francesco Nobili
We review the theory of Gradient Flows in the framework of convex and lower semicontinuous functionals on -spaces and prove that they can be characterized by the same…