9 citations · 20 across the 19 of their papers we have counts for
21 papers
Structural identification in general crystalline systems via Voronoi cell topology
Emanuel A. Lazar, Chris H. Rycroft
Widely used methods for identifying crystal structure in atomistic simulations are limited in practice to a handful of simple structures, leaving many important crystalline systems…
Sharp partial regularity of Hamiltonian stationary and special Lagrangian graphs
Arunima Bhattacharya, Gerard Orriols, Anna Skorobogatova
We prove a sharp partial regularity result for Hamiltonian stationary Lagrangian Lipschitz submanifolds in arbitrary smooth almost Kähler manifolds: every weak solution of the corr…
Minimizing clusters with prescribed asymptotic geometry
Robin Neumayer, Michael Novack, Anna Skorobogatova
We construct locally minimizing -clusters whose exterior interfaces are asymptotic to various prescribed singular area-minimizing cones. For , Bronsard & Novack…
On the geometric properties of multi-operator two-phase elliptic measure
Max Goering, Anna Skorobogatova
We provide a structural characterization of a given boundary using two-phase elliptic measure in a multi-operator setting, extending to this novel setting results of Kenig, Preiss…
On the non-uniqueness of locally minimizing clusters via singular cones
Lia Bronsard, Robin Neumayer, Michael Novack +1
We construct partitions of into three sets that locally minimize interfacial area among compactly supported volume…
Structure of two-dimensional mod area-minimizing currents near flat singularities: the codimension one case
Anna Skorobogatova, Luca Spolaor, Salvatore Stuvard
We obtain a fine structural result for two-dimensional mod area-minimizing currents of codimension one, close to flat singularities. Precisely, we show that, locally around an…
Hausdorff measure bounds for density- flat singularities of minimizing integral currents
Gianmarco Caldini, Anna Skorobogatova
In this article we prove that the set of flat singular points of locally highest density of area-minimizing integral currents of dimension and general codimension in a smooth R…
Free boundary regularity for semilinear variational problems with a topological constraint
Michael Novack, Daniel Restrepo, Anna Skorobogatova
We study a class of semilinear free boundary problems in which admissible functions have a topological constraint, or spanning condition, on their 1-level set. This constraint…
Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents
Paul Minter, Davide Parise, Anna Skorobogatova +1
We prove that the singular set of an -dimensional integral current in , semicalibrated by a -form is countably -rectifiable.…
Sobolev extension in a simple case
Marjorie Drake, Charles Fefferman, Kevin Ren +1
In this paper, we establish the existence of a bounded, linear extension operator when and is a finite subset of $\mathbb{R}^2…
Fine Structure of Singularities in Area-Minimizing Currents Mod
Camillo De Lellis, Paul Minter, Anna Skorobogatova
We study fine structural properties related to the interior regularity of -dimensional area minimizing currents mod in arbitrary codimension. We show: (i) the set of points…
Flat interior singularities for area almost-minimizing currents
Max Goering, Anna Skorobogatova
The interior regularity of area-minimizing integral currents and semi-calibrated currents has been studied extensively in recent decades, with sharp dimension estimates established…
Variational integrals on Hessian spaces: partial regularity for critical points
Arunima Bhattacharya, Anna Skorobogatova
We develop regularity theory for critical points of variational integrals defined on Hessian spaces of functions on open, bounded subdomains of , under compactly supp…
Rectifiability of flat singular points for area-minimizing mod hypercurrents
Anna Skorobogatova
Consider an -dimensional area minimizing mod current , with , inside a sufficiently regular Riemannian manifold of dimension . We show that the s…
The fine structure of the singular set of area-minimizing integral currents II: rectifiability of flat singular points with singularity degree larger than
Camillo De Lellis, Anna Skorobogatova
We consider an area-minimizing integral current of codimension higher than in a smooth Riemannian manifold . In a previous paper we have subdivided the set of interior s…
The Fine Structure of the Singular Set of Area-Minimizing Integral Currents III: Frequency 1 Flat Singular Points and -a.e. Uniqueness of Tangent Cones
Camillo De Lellis, Paul Minter, Anna Skorobogatova
We consider an area-minimizing integral current of codimension higher than 1 ins a smooth Riemannian manifold . We prove that has a unique tangent cone, which is a super…
The fine structure of the singular set of area-minimizing integral currents I: the singularity degree of flat singular points
Camillo De Lellis, Anna Skorobogatova
We consider an area-minimizing integral current of dimension and codimension at least and fix an arbitrary interior singular point where at least one tangent cone is fl…
An upper Minkowski bound for the interior singular set of area minimizing currents
Anna Skorobogatova
We show that for an area minimizing -dimensional integral current of codimension at least 2 inside a sufficiently regular Riemannian manifold, the upper Minkowski dimension…
Higher integrability for measures satisfying a PDE constraint
Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch +2
We establish higher integrability estimates for constant-coefficient systems of linear PDEs \[ \mathcal{A} μ= σ, \] where and are ve…
A look into some of the fine properties of functions with bounded -variation
Adolfo Arroyo-Rabasa, Anna Skorobogatova
We establish certain fine properties for functions of bounded -variation known in the classical setting. Here, is a th order constant-coefficient h…
Continuity and canceling operators of order on
Bogdan Raiţă, Anna Skorobogatova
We prove that for elliptic and canceling linear differential operators of order on , continuity of a map can be inferred from the fact that $\mat…