11 citations · 57 across the 19 of their papers we have counts for
22 papers
Insights from Autoresearch for Solar Panel Segmentation
Justinas Lekavicius, Kursat Komurcu, Valentas Gruzauskas +1
This paper investigates AutoResearch, a protocol in which a coding language model edits a training program under a one-hour GPU budget and retains a change only if validation IoU i…
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…
Extensions of Schoen--Simon--Yau and Schoen--Simon theorems via iteration à la De Giorgi
Costante Bellettini
We give an alternative proof of the Schoen--Simon--Yau curvature estimates and associated Bernstein-type theorems (1975), and extend the original result by including the case of $6…
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…
Embeddedness of liquid-vapour interfaces in stable equilibrium
Costante Bellettini
We consider a classical (capillary) model for a one-phase liquid in equilibrium. The liquid (e.g. water) is subject to a volume constraint, it does not mix with the surrounding vap…
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…
Multiplicity-1 minmax minimal hypersurfaces in manifolds with positive Ricci curvature
Costante Bellettini
We address the one-parameter minmax construction, via Allen--Cahn energy, that has recently lead to a new proof of the existence of a closed minimal hypersurface in an arbitrary co…
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…
Rate of decay for the mass ratio of pseudo-holomorphic integral 2-cycles
Costante Bellettini
We consider any pseudo holomorphic integral 2-cycle in an arbitrary almost complex manifold and perform a blow up analysis at an arbitrary point. Building upon a pseudo algebraic b…
Semi-calibrated 2-currents are pseudo holomorphic, with applications
Costante Bellettini
We show that any semi-calibration of degree 2 is locally induced by a smooth almost complex structure. We provide some applications of this result in the regularity theory for semi…
Compactness results for triholomorphic maps
Costante Bellettini, Gang Tian
We consider triholomorphic maps from an almost hyper-Hermitian manifold into a hyperKähler manifold . This means that satisfies…
Regularity of sets with constant horizontal normal in the Engel group
Costante Bellettini, Enrico Le Donne
In the Engel group with its Carnot group structure we study subsets of locally finite subRiemannian perimeter and possessing constant subRiemannian normal. We prove the rectifiabil…
Uniqueness of Tangent Cones to Positive-(p,p) Integral Cycles
Costante Bellettini
Let $(M, \om)$ be a symplectic manifold, endowed with a compatible almost complex structure J and the associated metric g . For any p \in {1, 2, ... (dim M)/2} the form $\Om := \fr…
Tangent cones to positive-(1,1) De Rham currents
Costante Bellettini
We consider positive-(1,1) De Rham currents in arbitrary almost complex manifolds and prove the uniqueness of the tangent cone at any point where the density does not have a jump w…
Almost complex structures and calibrated integral cycles in contact 5-manifolds
Costante Bellettini
In a contact manifold (M^5, alpha), we consider almost complex structures J which satisfy, for any vector v in the horizontal distribution, d alpha (v,Jv) = 0. We prove that integr…
The regularity of Special Legendrian Integral Cycles
Costante Bellettini, Tristan Riviere
Special Legendrian Integral Cycles in are the links of the tangent cones to Special Lagrangian integer multiplicity rectifiable currents in Calabi-Yau 3-folds. We show that s…