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 …

Suppose that M is a complete, embedded minimal surface in R 3 with an infinite number of
ends, finite genus, and compact boundary. We prove that the simple limit ends of M have …

Curvature estimates for constant mean curvature surfaces Page 1 CURVATURE ESTIMATES
FOR CONSTANT MEAN CURVATURE SURFACES WILLIAM H. MEEKS III and GIUSEPPE …

In this paper we show that a complete, embedded minimal surface in R 3, with finite topology
and one end, is conformal to a once-punctured compact Riemann surface. Moreover, using …

The number of constant mean curvature isometric immersions of a surface Page 1 Comment.
Math. Helv. 88 (2013), 163–183 DOI 10.4171/CMH/281 Commentarii Mathematici Helvetici © …

We consider two natural classes of minimal laminations in threemanifolds. Both classes may
be thought of as limits—in different senses—of embedded minimal disks. In both cases, we …

Given a closed flat 3-torus N, for each H> 0 and each non-negative integer g, we obtain area
estimates for closed surfaces with genus g and constant mean curvature H embedded in N …

The crowning achievement of this paper is the proof that round spheres are the only
complete, simply-connected surfaces embedded in R3 with nonzero constant mean …

In this paper we prove a theorem concerning lamination limits of sequences of compact
disks $ M_n $ embedded in $\mathbb {R}^ 3$ with constant mean curvature $ H_n $, when …