We present here a survey of recent spectacular successes in classical minimal surface
theory. We highlight this article with the theorem that the plane, the helicoid, the catenoid …

Meeks and Pérez extend their 2011 survey article" The classical theory of Minimal surfaces"
in the Bulletin of the American Mathematical Society to include other recent research results …

The topology and symmetry group of a free boundary minimal surface in the three-
dimensional Euclidean unit ball do not determine the surface uniquely. We provide pairs of …

We are interested in entire solutions of the Allen–Cahn equation u− F (u)= 0 which have
some special structure at infinity. In this equation, the function F is an even, double well …

In this paper, we prove even symmetry and monotonicity of certain solutions of Allen–Cahn
equation in a half plane. We also show that entire solutions with finite Morse index and four …

Given k≥ 2, we construct a (2k− 2)-parameter family of properly embedded minimal
surfaces in ℍ2× ℝ invariant by a vertical translation T, called saddle towers, which have total …

A solution of the Allen-Cahn equation in the plane is called a saddle solution if its nodal set
coincides with the coordinate axes. Such solutions are known to exist for a large class of …

It is classically known that the only entire zero-mean curvature graphs in the Euclidean 3-
space are planes, by Bernstein's theorem. A surface in Lorentz–Minkowski 3-space R 1 3 is …

We prove that a connected properly immersed minimal surface in ${\mathbb E}^ 3$ with
infinite symmetry group and area growth constant less than $3\pi $ is a plane, a catenoid, or …

An entire solution of the Allen–Cahn equation Δ u= f (u), where f is an odd function and has
exactly three zeros at±1 and 0, for example, f (u)= u (u 2− 1), is called a 2 k-end solution if its …