Related papers: Calibrating Forms for Minimal Graphs in Arbitrary …
This paper presents a complete classification of minimal graph surfaces that admit graphical transformations into other minimal surfaces. These transformations are functions that map the height function of a minimal graph surface to another…
In this paper, we study the differential inclusion associated to the minimal surface system for two-dimensional graphs in $\mathbb{R}^{2 + n}$. We prove regularity of $W^{1,2}$ solutions and a compactness result for approximate solutions of…
We study the problem of finding a minimal graph with prescribed boundary data in arbitrary dimension and codimension. Existence, uniqueness, stability and regularity are treated. We first present the well-known results for codimension one:…
Let \Sigma be a minimal submanifold of \R^{n+m} that can be represented as the graph of a smooth map f:\R^n-->\R^m. We apply a formula we derived in the study of mean curvature flow to obtain conditions under which \Sigma must be an affine…
Let $\mathbb{E}$ be a connected and orientable Riemannian 3-manifold with a non-singular Killing vector field whose associated one-parameter group of the isometries of $\mathbb{E}$ acts freely and properly on $\E$. Then, there exists a…
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…
Inspired by the prospect of having discretized spaces emerge from random graphs, we construct a collection of simple and explicit exponential random graph models that enjoy, in an appropriate parameter regime, a roughly constant vertex…
In this paper we extend a recent result of Collin-Rosenberg ({\it a solution to the minimal surface equation in the Euclidean disc has radial limits almost everywhere}) to a large class of differential operators in Divergence form.…
The combinatorial refinement techniques have proven to be an efficient approach to isomorphism testing for particular classes of graphs. If the number of refinement rounds is small, this puts the corresponding isomorphism problem in a…
Let $(M, g)$ be a compact real analytic Riemannian manifold and $\pi \colon \widetilde{M} \to M$ its universal cover. Assume that $\widetilde{M}$ can be realised as a manifold definable in an o-minimal structure $\Sigma$ expanding…
We construct non-flat minimal capillary cones with bi-orthogonal symmetry groups for any dimension and contact angle. These cones interpolate between rescalings of a singular solution to the one-phase problem and the free-boundary cone…
We define holomorphic quadratic differentials for spacelike surfaces with constant mean curvature in the Lorentzian homogeneous spaces $\mathbb{L}(\kappa,\tau)$ with isometry group of dimension 4, which are dual to the Abresch-Rosenberg…
A set of n non-collinear points in the Euclidean plane defines at least n different lines. Chen and Chv\'tal in 2008 conjectured that the same results is true in metric spaces for an adequate definition of line. More recently, it was…
We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that…
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are…
This paper introduces a new extension of Riemannian elastic curve matching to a general class of geometric structures, which we call (weighted) shape graphs, that allows for shape registration with partial matching constraints and…
Modular graph forms are a class of modular covariant functions which appear in the genus-one contribution to the low-energy expansion of closed string scattering amplitudes. Modular graph forms with holomorphic subgraphs enjoy the…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
We define, for any graph $G=(V,E)$, a boundary $\partial G \subseteq V$. The definition coincides with what one would expected for the discretization of (sufficiently nice) Euclidean domains and contains all vertices from the…
We consider a family of non-compact manifolds $X_\eps$ (``graph-like manifolds'') approaching a metric graph $X_0$ and establish convergence results of the related natural operators, namely the (Neumann) Laplacian $\laplacian {X_\eps}$ and…