Related papers: Minimal surfaces with mixed three-form flux

This paper gives sharp linear bounds on the genus of a normal surface in a triangulated compact, orientable 3--manifold in terms of the quadrilaterals in its cell decomposition---different bounds arise from varying hypotheses on the surface…

We study minimal graphs in the homogeneous Riemannian 3-manifold $\widetilde{PSL_2(\mathbb{R})}$ and we give examples of invariant surfaces. We derive a gradient estimate for solutions of the minimal surface equation in this space and…

Minimal surfaces in closed 3-manifolds are classically constructed via the Almgren-Pitts approach. The Allen-Cahn approximation has proved to be a powerful alternative, and Chodosh and Mantoulidis (in Ann. Math. 2020) used it to give a new…

Let Y be a surface with only finitely many singularities all of which are cusps. A set of cusps on Y is called three-divisible, if there is a cyclic global triple cover of Y branched precisely over these cusps. The aim of this note is to…

We show the existence of a smooth solution for the flow deformed by the square root of the scalar curvature multiplied by a positive anisotropic factor $\psi$ given a strictly convex initial hypersurface in Euclidean space suitably pinched.…

We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection…

Let $\alpha$ be a polygonal Jordan curve in $\bfR^3$. We show that if $\alpha$ satisfies certain conditions, then the least-area Douglas-Rad\'{o} disk in $\bfR^3$ with boundary $\alpha$ is unique and is a smooth graph. As our conditions on…

We discuss timelike and spacelike minimal surfaces in $AdS_n$ using a Pohlmeyer type reduction. The differential equations for the reduced system are derived in a parallel treatment of both type of surfaces, with emphasis on their…

Nominal two-dimensional (2D) shear layers have been studied extensively, and their principal dynamics are well understood. In practical configurations, however, the behavior of such shear layers is affected by proximal surfaces. In this…

For exact area-preserving twist maps, curves were constructed through the gaps of cantori in \cite{MMP84}, which were conjectured to have minimal flux subject to passing through the points of the cantorus. It was pointed out by \cite{Pol}…

We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in [9], wherein the…

In this paper, we give an improved Morse index bound of minimal hypersurfaces from Almgren-Pitts min-max construction in any closed Riemannian manifold $M^{n+1}$ $(n+1 \geq 3$), which generalizes a result by X. Zhou…

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.…

Context. The potential field source surface model is frequently used as a basis for further scientific investigations where a comprehensive coronal magnetic field is of importance. Its parameters, especially the position and shape of the…

Let M be a compact, orientable, mean convex 3-manifold with boundary. We show that the set of all simple closed curves in the boundary of M which bound unique area minimizing disks in M is dense in the space of simple closed curves in the…

Let $\mathcal X\to\mathbb D$ be a flat family of projective complex 3-folds over a disc $\mathbb D$ with smooth total space $\mathcal X$ and smooth general fibre $\mathcal X_t,$ and whose special fiber $\mathcal X_0$ has double normal…

A minimal surface in a random environment (MSRE) is a $d$-dimensional surface in $(d+n)$-dimensional space which minimizes the sum of its elastic energy and its environment potential energy, subject to prescribed boundary values. Apart from…

We study the quantization of the 6d Seiberg-Witten curve for D-type minimal conformal matter theories compactified on a two-torus. The quantized 6d curve turns out to be a difference equation established via introducing codimension two and…

The conformal structure on minimal surfaces plays a key role in studying the properties of minimal surfaces. Here we extend the results of uniformization of surfaces with boundary to get the (weak) uniformization results for triple junction…

We present integral equations for the area of minimal surfaces in AdS_3 ending on generic smooth boundary contours. The equations are derived from the continuum limit of the AMSV result for null polygonal boundary contours. Remarkably these…