53 citations · 135 across the 23 of their papers we have counts for
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Generic finiteness of minimal surfaces with bounded Morse index
Alessandro Carlotto
Given a compact 3-manifold N without boundary, we prove that for a bumpy metric of positive scalar curvature the space of minimal surfaces having a uniform upper bound on the Morse…
Compactness of the space of minimal hypersurfaces with bounded volume and p-th Jacobi eigenvalue
Lucas Ambrozio, Alessandro Carlotto, Ben Sharp
Given a closed Riemannian manifold of dimenion less than eight, we prove a compactness result for the space of closed, embedded minimal hypersurfaces satisfying a volume bound and…
Minimal hyperspheres of arbitrarily large Morse index
Alessandro Carlotto
We show that the Morse index of a closed minimal hypersurface in a four-dimensional Riemannian manifold cannot be bound in terms of the volume and the topological invariants of the…
Effective versions of the positive mass theorem
Alessandro Carlotto, Otis Chodosh, Michael Eichmair
The study of stable minimal surfaces in Riemannian -manifolds with non-negative scalar curvature has a rich history. In this paper, we prove rigidity of such surfaces w…