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 …

We study relationships between stability of constant mean curvature surfaces in a
Riemannian three-manifold N and the geometry of leaves of laminations and foliations of N …

Based on work of Daniel and Mira, we prove that for each $ H0 $, there exists a unique (up
to ambient isometry) immersed constant mean curvature $ H $ sphere $ S_H $ in ${\rm Sol} …

In this paper, we study the global geometry of complete, constant mean curvature
hypersurfaces embedded in $ n $-manifolds. More precisely, we give conditions that imply …

Given a non-compact, simply connected homogeneous three-manifold X and a sequence {Ω
n} n of isoperimetric domains in X with volumes tending to infinity, we prove that, as n→∞:(1) …

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 © …

In this paper, we prove rigidity of certain complete surfaces embedded in with constant mean
curvature. We also show that for certain complete surfaces embedded in with constant mean …

In this paper we review four curvature estimates for constant mean curvature surfaces in R3.
They are the Schoen Curvature Estimate, the Choi-Schoen Curvature Estimate, the One …

In this paper we generalize the Dynamics Theorem for nonzero CMC surfaces in R^ 3 to a
new Dynamics Theorem for nonzero CMC hyper-surfaces in a homogeneous manifold. In …

The paper treats the isometric deformability of non-simply-connected constant mean
curvature surfaces which are neither assumed embedded nor complete. We prove that if a …