Michele Rimoldi

Ricci almost solitons

We introduce a natural extension of the concept of gradient Ricci soliton: the Ricci almost soliton. We provide existence and rigidity results, we deduce a-priori curvature estimates and isolation phenomena, and we investigate some topological properties. A number of differential identities involving the relevant geometric quantities are derived. Some basic tools from the weighted manifold theory such as general weighted volume comparisons and maximum principles at infinity for diffusion operators are discussed.

Stability properties and topology at infinity of \(f\)-minimal hypersurfaces

We study stability properties of

Topology of steady and expanding gradient Ricci solitons via f-harmonic maps

f

Complete self-shrinkers confined into some regions of the space

f-minimal hypersurfaces isometrically immersed in weighted manifolds with non-negative Bakry–Émery Ricci curvature under volume growth conditions. Moreover, exploiting a weighted version of a finiteness result and the adaptation to this setting of Li–Tam theory, we investigate the topology at infinity of

Rigidity results and topology at infinity of translating solitons of the mean curvature flow

f

A remark on Einstein warped products

f-minimal hypersurfaces. On the way, we prove a new comparison result in weighted geometry and we provide a general weighted