3 citations · 3 across the 3 of their papers we have counts for
7 papers
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…
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…