13 citations · 62 across the 19 of their papers we have counts for
19 papers
Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency 2, higher order asymptotics, and the local topology
Brian Krummel, Neshan Wickramasekera
This is the third part in a series of papers developing a new framework to study the local structure of -dimensional area-minimizing rectifiable currents of codimension $\ge…
A Branch Set Stratification for Stationary Varifolds with Epsilon-Regularity
Brian Krummel, Paul Minter, Neshan Wickramasekera
Suppose is a class of stationary integral -varifolds in which is closed under weak limits, homotheties, rotations, and disjoi…
On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes
Spencer Becker-Kahn, Paul Minter, Neshan Wickramasekera
We study stationary integral -varifolds in the unit ball . Allard's regularity theorem establishes the existence of for w…
Analysis of singularities of area minimizing currents, Part I: planar frequency, branch points of rapid decay, and weak locally uniform approximation
Brian Krummel, Neshan Wickramasekera
This is the first paper in a series developing a new framework for -dimensional area-minimizing rectifiable currents of codim. . Our approach relies on an intrinsic…
Analysis of singularities of area-minimizing currents, Part II: a uniform height bound, estimates away from branch points of rapid decay, and uniqueness of tangent cones
Brian Krummel, Neshan Wickramasekera
This is the second paper in a series developing a new framework for -dimensional area-minimizing rectifiable currents of codimension . In the present article we esta…
Fine properties of branch point singularities: stationary two-valued graphs and stable minimal hypersurfaces near points of density
Brian Krummel, Neshan Wickramasekera
We study (higher order) asymptotic behaviour near branch points of stationary -dimensional two-valued graphs in an open subset of . Specifically, i…
A Structure Theory for Stable Codimension 1 Integral Varifolds with Applications to Area Minimising Hypersurfaces mod p
Paul Minter, Neshan Wickramasekera
For any , we establish a structure theory for the class of stable codimension 1 stationary integral varifolds admitting…
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…
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…
Fine properties of branch point singularities: Dirichlet energy minimizing multi-valued functions
Brian Krummel, Neshan Wickramasekera
In the early 1980's Almgren developed a theory of Dirichlet energy minimizing multi-valued functions, proving that the Hausdorff dimension of the singular set (including branch poi…
The blow up method for Brakke flows: networks near triple junctions
Yoshihiro Tonegawa, Neshan Wickramasekera
We introduce a parabolic blow-up method to study the asymptotic behavior of an integral Brakke flow of planar networks (i.e. a 1-dimensional integral Brakke flow in a two dimension…
Fine properties of branch point singularities: Two-valued harmonic functions
Brian Krummel, Neshan Wickramasekera
In the 1980's, Almgren developed a theory of multi-valued Dirichlet energy minimizing functions on dimensional domains and used it, in an essential way, to bound the Hausdorff…
A sharp strong maximum principle and a sharp unique continuation theorem for singular minimal hypersurfaces
Neshan Wickramasekera
We prove the two theorems of the title, settling two long standing questions in the local theory of singular minimal hypersurfaces. The sharpness of either result is with respect t…
A frequency function and singular set bounds for branched minimal immersions
Leon Simon, Neshan Wickramasekera
We show that any 2-valued C^{1, α} (α\in (0, 1)) function u = {u_{1}, u_{2}} on an open ball B in {\mathbb R}^{n} with values u_{1}, u_{2} \in {\mathbb R}^{k} whose graph, viewed a…
Stable phase interfaces in the van der Waals--Cahn--Hilliard theory
Yoshihiro Tonegawa, Neshan Wickramasekera
We prove that any limit-interface corresponding to a locally uniformly bounded, locally energy-bounded sequence of stable critical points of the van der Waals--Cahn--Hilliard energ…
A general regularity theory for stable codimension 1 integral varifolds
Neshan Wickramasekera
We give a necessary and sufficient geometric structural condition for a stable codimension 1 integral varifold on a smooth Riemannian manifold to correspond to an embedded smooth h…
A regularity and compactness theory for immersed stable minimal hypersurfaces of multiplicity at most 2
Neshan Wickramasekera
We prove that a stable minimal hypersurface of an open ball having a singular set of locally finite codimension 2 Hausdorff measure which is weakly close to a multiplicity 2 hyperp…