Related papers: A Variational Characterization of the Catenoid

Lawson and Osserman proved that the Dirichlet problem for the minimal surface system is not always solvable in the class of Lipschitz maps. However, it is known that minimizing sequences (for area) of Lipschitz graphs converge to objects…

We first consider a uniqueness problem for embedded free boundary minimal annuli in the three-dimensional Euclidean unit half-ball. Then, we obtain symmetry properties for compact embedded free boundary minimal surfaces in the unit ball.…

Motivated by the large ammount of results obtained for minimal and positive constant mean curvature surfaces in several ambient spaces, the aim of this paper is to obtain half-space theorems for properly immersed surfaces in $\mathbb{R}^3$…

We show that asymptotically Schwarzschildean 3-manifolds cannot contain minimal surfaces obtained by perturbative deformations of a Euclidean catenoid, no matter how small the ADM mass of the ambient space and how large the neck of the…

This paper introduces a geometrically constrained variational problem for the area functional. We consider the area restricted to the langrangian surfaces of a Kaehler surface, or, more generally, a symplectic 4-manifold with suitable…

In this paper we use the Alexandrov Reflection Method to obtain a characterization to embedded CMC capillary annulus $\Sigma^2 \subset \mathbb{B}^3$. In especial, but using a new strategy, we present a new characterization to the critical…

Given a compact closed subset $M$ of a line segment in $\mathbb{R}^3$, we construct a sequence of minimal surfaces $\Sigma_k$ embedded in a neighborhood $C$ of the line segment that converge smoothly to a limit lamination of $C$ away from…

In this paper, we prove the existence of minimizers of a class of multi-constrained variational problems. We consider systems involving a nonlinearity that does not satisfy compactness, monotonicity, neither symmetry properties. Our…

We prove that closed surfaces of all topological types, except for the non-orientable odd-genus ones, can be minimally embedded in the Riemannian product of a sphere and a circle of arbitrary radius. We illustrate it by obtaining some…

Given two Jordan curves in a Riemannian manifold, a minimal surface of annulus type bounded by these curves is described as the harmonic extension of a critical point of some functional (the Dirichlet integral) in a certain space of…

Minimal surface problems arise naturally in many soft matter systems whose free energies are dominated by surface or interface energies. Of particular interest are the shapes, stability and mechanical stresses of minimal surfaces spanning…

It is proved that smooth closed curves of given length minimizing the principal eigenvalue of the Schr\"odinger operator $-\frac{d^2}{ds^2}+\kappa^2$ exist. Here $s$ denotes the arclength and $\kappa$ the curvature. These minimizers are…

A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically. It is proved under general assumptions that the support of a minimizing measure is either completely timelike, or…

We introduce a new family of closed differential forms naturally associated with minimal graphical submanifolds in Euclidean space, defined in arbitrary codimension. For each minimal graph, we construct an explicit closed form whose…

We develop a theory of "minimal $\theta$-graphs" and characterize the behavior of limit laminations of such surfaces, including an understanding of their limit leaves and their curvature blow-up sets. We use this to prove that it is…

In this note, we prove a Schwarz-Pick type lemma for minimal maps between negatively curved Riemannian surfaces. More precisely, we prove that if $f:M \to N$ is a minimal map with bounded Jacobian between two complete negatively curved…

Motivated by the study of the non-parametric area $\mathcal A$ of the graph of the vortex map $u$ (a two-codimensional singular surface in $\mathbb R^4$) over the disc $\Omega \subset \mathbb R^2$ of radius $l$, we perform a careful…

We construct families of embedded, singly periodic minimal surfaces of any genus $g$ in the quotient with any even number $2n>2$ of almost parallel Scherk ends. A surface in such a family looks like $n$ parallel planes connected by $n-1+g$…

We construct a Riemannian metric $g$ on $\mathbb{R}^4$ (arbitrarily close to the euclidean one) and a smooth simple closed curve $\Gamma\subset \mathbb R^4$ such that the unique area minimizing surface spanned by $\Gamma$ has infinite…

We prove a local minimizing property for strictly stable free-boundary minimal hypersurfaces in the relative current setting. Let $\Sigma^n$ be a compact, two-sided, properly embedded free-boundary minimal hypersurface in a compact…