56 citations · 125 across the 13 of their papers we have counts for
15 papers
Isoperimetric and Michael-Simon inequalities on manifolds with asymptotically nonnegative curvature
Debora Impera, Stefano Pigola, Michele Rimoldi +1
We establish the validity of the isoperimetric inequality (or equivalently, an Euclidean-type Sobolev inequality) on manifolds with asymptotically non-negative sectional curv…
Asymptotically non-negative Ricci curvature, elliptic Kato constant and isoperimetric inequalities
Debora Impera, Michele Rimoldi, Giona Veronelli
The ABP method for proving isoperimetric inequalities has been first employed by Cabré in , then developed by Brendle, notably in the context of non-compact Riemannia…
Poincaré inequality and topological rigidity of translators and self-expanders for the mean curvature flow
Debora Impera, Michele Rimoldi
We prove an abstract structure theorem for weighted manifolds supporting a weighted -Poincaré inequality and whose ends satisfy a suitable non-integrability condition. We then s…
Rigidity and non-existence results for collapsed translators
Debora Impera, Niels Martin Møller, Michele Rimoldi
We prove a rigidity result for mean curvature self-translating solitons, characterizing the grim reaper cylinder as the only finite entropy self-translating 2-surface in $\mathbb{R…
Density and non-density of on complete manifolds with curvature bounds
Shouhei Honda, Luciano Mari, Michele Rimoldi +1
We investigate the density of compactly supported smooth functions in the Sobolev space on complete Riemannian manifolds. In the first part of the paper, we extend to the…
Higher order distance-like functions and Sobolev spaces
Debora Impera, Michele Rimoldi, Giona Veronelli
We consider complete Riemannian manifolds with a controlled growth of the covariant derivatives of Ricci curvatures up to order and a controlled decay of the injectivity radi…
Index and first Betti number of f-minimal hypersurfaces: general ambients
Debora Impera, Michele Rimoldi
We generalize a method by L. Ambrozio, A. Carlotto, and B. Sharp to study the Morse index of closed f-minimal hypersurfaces isometrically immersed in a general weighted manifold. T…
Density problems for second order Sobolev spaces and cut-off functions on manifolds with unbounded geometry
Debora Impera, Michele Rimoldi, Giona Veronelli
We consider complete non-compact manifolds with either a sub-quadratic growth of the norm of the Riemann curvature, or a sub-quadratic growth of both the norm of the Ricci curvatur…
Quantitative index bounds for translators via topology
Debora Impera, Michele Rimoldi
We obtain a quantitative estimate on the generalised index of translators for the mean curvature flow with bounded norm of the second fundamental form. The estimate involves the di…
Index and first Betti number of -minimal hypersurfaces and self-shrinkers
Debora Impera, Michele Rimoldi, Alessandro Savo
We study the Morse index of self-shrinkers for the mean curvature flow and, more generally, of -minimal hypersurfaces in a weighted Euclidean space endowed with a convex weight.…
Extremals of Log Sobolev inequality on non-compact manifolds and Ricci soliton structures
Michele 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…
Rigidity results and topology at infinity of translating solitons of the mean curvature flow
Debora Impera, Michele Rimoldi
In this paper we obtain rigidity results and obstructions on the topology at infinity of translating solitons of the mean curvature flow in the Euclidean space. Our approach relies…
Stability properties and topology at infinity of f-minimal hypersurfaces
Debora Impera, Michele Rimoldi
We study stability properties of -minimal hypersurfaces isometrically immersed in weighted manifolds with non-negative Bakry-Emery Ricci curvature under volume growth conditions…
Topology of steady and expanding gradient Ricci solitons via f-harmonic maps
Michele Rimoldi, Giona Veronelli
In this paper we give some results on the topology of manifolds with -Bakry-Émery Ricci tensor bounded below, and in particular of steady and expanding gradient Ricci solit…
Myers' type theorems and some related oscillation results
Paolo Mastrolia, Michele Rimoldi, Giona Veronelli
In this paper we study the behavior of solutions of a second order differential equation. The existence of a zero and its localization allow us to get some compactness results. In…