https://neckpinch.com/authors/giona-veronelli/New arXiv papers by Giona Veronelli, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1605.09240/arxiv:1605.09240Mon, 30 May 2016 00:00:00 GMTMichele Rimoldi, Giona Veronelli — In this paper we establish the existence of extremals for the Log Sobolev functional on complete non-compact manifolds with Ricci curvature bounded from below and strictly positive injectivity radius, under a condition near infinity. When Ricci curvature is also bounded from above we get exponential decay at infinity of the extremals. As a consequence of these analytical results we establish, under the same assumptions, that non-trivial shrinking Ricci solitons support a gradient Ricci soliton structure. On the way, we prove two results of independent interest: the existence of a distance-like function with uniformly controlled gradient and Hessian on complete non-compact manifolds with bounded Ricci curvature and strictly positive injectivity radius and a general growth estimate for the norm of the soliton vector field on manifolds with bounded Ricci curvature.Ricci solitonsPerelman entropyBoundaries & non-compact