56 citations · 141 across the 19 of their papers we have counts for
5 papers · 2 filters
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.…
The Frankel property for self-shrinkers from the viewpoint of elliptic PDE's
Debora Impera, Stefano Pigola, Michele Rimoldi
We show that two properly embedded self-shrinkers in Euclidean space that are sufficiently separated at infinity must intersect at a finite point. The proof is based on a localized…