4 papers
Inequivalent complexity criteria for free boundary minimal surfaces
Alessandro Carlotto, Giada Franz
We obtain a series of results in the global theory of free boundary minimal surfaces, which in particular provide a rather complete picture for the way different complexity criteri…
Contractibility results for certain spaces of Riemannian metrics on the disc
Alessandro Carlotto, Damin Wu
We provide a general contractibility criterion for subsets of Riemannian metrics on the disc. For instance, this result applies to the space of metrics that have positive Gauss cur…
Compactness analysis for free boundary minimal hypersurfaces
Lucas Ambrozio, Alessandro Carlotto, Ben Sharp
We investigate compactness phenomena involving free boundary minimal hypersurfaces in Riemannian manifolds of dimension less than eight. We provide natural geometric conditions tha…
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…