In this paper we solve two open problems of classical surface theory; we give an affirmative
answer to a 1956 conjecture by AD Alexandrov on the uniqueness of immersed spheres in …

This survey paper investigates, from a purely geometric point of view, Daniel's isometric
conjugation between minimal and constant mean curvature surfaces immersed in …

We develop a global theory for complete hypersurfaces in $\mathbb {R}^{n+ 1} $ whose
mean curvature is given as a prescribed function of its Gauss map. This theory extends the …

Minimal translation surfaces in the Heisenberg group Nil3 Page 1 Geom Dedicata (2012)
161:221–231 DOI 10.1007/s10711-012-9702-8 ORIGINAL PAPER Minimal translation surfaces …

A Killing submersion is a Riemannian submersion from an orientable 3-manifold to an
orientable surface whose fibers are the integral curves of a unit Killing vector field in the 3 …

Let M be a simply connected homogeneous three-manifold with isometry group of
dimension 4, and let Σ be any compact surface of genus zero immersed in M whose mean …

In this paper, we prove a general halfspace theorem for constant mean curvature surfaces.
Under certain hypotheses, we prove that, in an ambient space $ M^ 3$, any constant mean …

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 …

In this note, we determine all the homogeneous structures on non-symmetric three-
dimensional Riemannian Lie groups. We show that a non-symmetric three-dimensional …

We provide an explicit classification of the following four families of surfaces in any
homogeneous 3-manifold with 4-dimensional isometry group: isoparametric surfaces …