In these notes we present some aspects of the basic theory on the geometry of a three-
dimensional simply-connected Lie group X endowed with a left invariant metric. This …

In this paper we prove a local removable singularity theorem for certain minimal laminations
with isolated singularities in a Riemannian three-manifold. This removable singularity …

We prove that two spheres of the same constant mean curvature in an arbitrary
homogeneous three-manifold only differ by an ambient isometry, and we determine the …

Suppose $ L $ is a lamination of a Riemannian manifold by hypersurfaces with the same
constant mean curvature $ H $. We prove that every limit leaf of $ L $ is stable for the Jacobi …

We prove a chord arc type bound for disks embedded in ℝ 3 with constant mean curvature
that does not depend on the value of the mean curvature. This bound is inspired by and …

Abstract We generalize Meeks and Yau's embeddedness result on the solutions of the
Plateau problem to constant mean curvature disks. We show that any minimizing H-disk in …

In this paper we study the geometry of complete constant mean curvature (CMC)
hypersurfaces immersed in an (n+ 1)-dimensional Riemannian manifold N (n= 2, 3 and 4) …

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 generalize our previous Local Removable Singularity Theorem for minimal
laminations to the case of weak $ H $-laminations (with $ H\in {\Bbb R} $ constant) in a …