53 citations · 135 across the 23 of their papers we have counts for
34 papers
Observing minimal submanifolds with isolated singularities on open sets of metrics
Alessandro Carlotto, Yangyang Li, Zhihan Wang
We develop a perturbative theory for minimal submanifolds with only (strongly) isolated singularities, with respect to varying background Riemannian metrics. As an application, we…
Non-persistence of strongly isolated singularities, and geometric applications
Alessandro Carlotto, Yangyang Li, Zhihan Wang
We obtain a generic regularity result for stationary integral -varifolds with only strongly isolated singularities inside -dimensional Riemannian manifolds, in absence of any…
Index growth not imputable to topology
Alessandro Carlotto, Mario B. Schulz, David Wiygul
We employ partitioning methods, in the spirit of Montiel--Ros but here recast for general actions of compact Lie groups, to prove effective lower bounds on the Morse index of certa…
Disc stackings and their Morse index
Alessandro Carlotto, Mario B. Schulz, David Wiygul
We construct free boundary minimal disc stackings, with any number of strata, in the three-dimensional Euclidean unit ball, and prove uniform, linear lower and upper bounds on the…
Attaching faces of positive scalar curvature manifolds with corners
Alessandro Carlotto, Chao Li
We prove a novel desingularization theorem, that allows to smoothly attach two given manifolds with corners by suitably gluing a pair of isometric faces, with control on both the s…
A Note about Isotopy and Concordance of Positive Scalar Curvature Metrics on Compact Manifolds with Boundary
Alessandro Carlotto, Chao Li
We study notions of isotopy and concordance for Riemannian metrics on manifolds with boundary and, in particular, we introduce two variants of the concept of minimal concordance, t…
Spectral estimates for free boundary minimal surfaces via Montiel-Ros partitioning methods
Alessandro Carlotto, Mario B. Schulz, David Wiygul
We adapt and extend the Montiel-Ros methodology to compact manifolds with boundary, allowing for mixed (including oblique) boundary conditions and also accounting for the action of…
Infinitely many pairs of free boundary minimal surfaces with the same topology and symmetry group
Alessandro Carlotto, Mario B. Schulz, David Wiygul
The topology and symmetry group of a free boundary minimal surface in the three-dimensional Euclidean unit ball do not determine the surface uniquely. We provide pairs of non-isome…
Minimal hypertori in the four-dimensional sphere
Alessandro Carlotto, Mario B. Schulz
We prove that the four-dimensional round sphere contains a minimally embedded hypertorus, as well as infinitely many, pairwise non-isometric, immersed ones. Our analysis also yield…
Constrained deformations of positive scalar curvature metrics, II
Alessandro Carlotto, Chao Li
We prove that various spaces of constrained positive scalar curvature metrics on compact 3-manifolds with boundary, when not empty, are contractible. The constraints we mostly focu…
Free boundary minimal surfaces with connected boundary and arbitrary genus
Alessandro Carlotto, Giada Franz, Mario B. Schulz
We employ min-max techniques to show that the unit ball in contains embedded free boundary minimal surfaces with connected boundary and arbitrary genus.
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…
Constrained deformations of positive scalar curvature metrics
Alessandro Carlotto, Chao Li
We present a series of results concerning the interplay between the scalar curvature of a manifold and the mean curvature of its boundary. In particular, we give a complete topolog…
Bubbling analysis and geometric convergence results for free boundary minimal surfaces
Lucas Ambrozio, Reto Buzano, Alessandro Carlotto +1
We investigate the limit behaviour of sequences of free boundary minimal hypersurfaces with bounded index and volume, by presenting a detailed blow-up analysis near the points wher…
Geometric convergence results for closed minimal surfaces via bubbling analysis
Lucas Ambrozio, Reto Buzano, Alessandro Carlotto +1
We present some geometric applications, of global character, of the bubbling analysis developed by Buzano and Sharp for closed minimal surfaces, obtaining smooth multiplicity one c…
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…
A note on the index of closed minimal hypersurfaces of flat tori
Lucas Ambrozio, Alessandro Carlotto, Ben Sharp
Generalizing earlier work by Ros in ambient dimension three, we prove an affine lower bound for the Morse index of closed minimal hypersurfaces inside a flat torus in terms of thei…
Min-max embedded geodesic lines in asymptotically conical surfaces
Alessandro Carlotto, Camillo De Lellis
We employ min-max methods to construct uncountably many, geometrically distinct, properly embedded geodesic lines in any asymptotically conical surface of non-negative scalar curva…
A non-existence result for minimal catenoids in asymptotically flat spaces
Alessandro Carlotto, Andrea Mondino
We show that asymptotically Schwarzschildean 3-manifolds cannot contain minimal surfaces obtained by perturbative deformations of a Euclidean catenoid, no matter how small the ADM…
Index estimates for free boundary minimal hypersurfaces
Lucas Ambrozio, Alessandro Carlotto, Ben Sharp
We show that the Morse index of a properly embedded free boundary minimal hypersurface in a strictly mean convex domain of the Euclidean space grows linearly with the dimension of…
Comparing the Morse index and the first Betti number of minimal hypersurfaces
Lucas Ambrozio, Alessandro Carlotto, Ben Sharp
By extending and generalising previous work by Ros and Savo, we describe a method to show that the Morse index of every closed minimal hypersurface on certain positively curved amb…
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…