11 citations · 57 across the 19 of their papers we have counts for
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Smooth approximations for constant-mean-curvature hypersurfaces with isolated singularities
Costante Bellettini, Konstantinos Leskas
We consider a CMC hypersurface with an isolated singular point at which the tangent cone is regular, and such that, in a neighbourhood of said point, the hypersurface is the bounda…
On isolated singularities and generic regularity of min-max CMC hypersurfaces
Costante Bellettini, Kobe Marshall-Stevens
In compact Riemannian manifolds of dimension 3 or higher with positive Ricci curvature, we prove that every constant mean curvature hypersurface produced by the Allen-Cahn min-max…
Embeddedness of Min-Max CMC Hypersurfaces in Manifolds with Positive Ricci Curvature
Costante Bellettini, Myles Workman
We prove that on a compact Riemannian manifold of dimension or higher, with positive Ricci curvature, the Allen--Cahn min-max scheme (implemented by the first author and N. Wic…
Hypersurfaces with mean curvature prescribed by an ambient function: compactness results
Costante Bellettini
We consider, in a first instance, the class of boundaries of sets with locally finite perimeter whose (weakly defined) mean curvature is , for a given continuous positive ambi…
Generic existence of multiplicity-1 minmax minimal hypersurfaces via Allen--Cahn
Costante Bellettini
In Guaraco's 2018 work a new proof was given of the existence of a closed minimal hypersurface in a compact Riemannian manifold with . This was achieved by emplo…
The inhomogeneous Allen--Cahn equation and the existence of prescribed-mean-curvature hypersurfaces
Costante Bellettini, Neshan Wickramasekera
We prove that for any given compact Riemannian manifold of dimension and any non-negative Lipschitz function on , there exists a quasi-embedded, boundaryles…
Sets with constant normal in Carnot groups: properties and examples
Costante Bellettini, Enrico Le Donne
We analyze subsets of Carnot groups that have intrinsic constant normal, as they appear in the blowup study of sets that have finite sub-Riemannian perimeter. The purpose of this p…
Stable prescribed-mean-curvature integral varifolds of codimension 1: regularity and compactness
Costante Bellettini, Neshan Wickramasekera
In a previous paper we developed a regularity and compactness theory in Euclidean ambient spaces for codimension 1 weakly stable CMC integral varifolds satisfying two (necessary) s…
Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces
Costante Bellettini, Otis Chodosh, Neshan Wickramasekera
Weakly stable constant mean curvature (CMC) hypersurfaces are stable critical points of the area functional with respect to volume preserving deformations. We establish a pointwise…
Stable CMC integral varifolds of codimension : regularity and compactness
Costante Bellettini, Neshan Wickramasekera
We give two structural conditions on a codimension integral -varifold with first variation locally summable to an exponent that imply the following: whenever each orie…