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Rotationally invariant constant mean curvature surfaces in homogeneous 3-manifolds

- Francisco Torralbo
- Mathematics
- 26 November 2009

Abstract We classify constant mean curvature surfaces invariant by a 1-parameter group of isometries in the Berger spheres and in the special linear group Sl ( 2 , R ) . In particular, all constant… Expand

Compact minimal surfaces in the Berger spheres

- Francisco Torralbo
- Mathematics
- 7 July 2010

In this article, we construct compact, arbitrary Euler characteristic, orientable and non-orientable minimal surfaces in the Berger spheres. Also, we show an interesting family of surfaces that are… Expand

On stable compact minimal submanifolds

- Francisco Torralbo, F. Urbano
- Mathematics
- 3 December 2010

Stable compact minimal submanifolds of the product of a sphere and any Riemannian manifold are classified whenever the dimension of the sphere is at least three. The complete classification of the… Expand

Compact stable constant mean curvature surfaces in homogeneous 3-manifolds

- Francisco Torralbo, F. Urbano
- Mathematics
- 2012

We classify the stable constant mean curvature spheres in the homogeneous Riemannian 3-manifolds: the Berger spheres, the special linear group and the Heisenberg group. We show that all of them are… Expand

Compact stable constant mean curvature surfaces in the Berger spheres

- Francisco Torralbo, F. Urbano
- Mathematics
- 8 June 2009

In the 1-parameter family of Berger spheres S^3(a), a > 0 (S^3(1) is the round 3-sphere of radius 1) we classify the stable constant mean curvature spheres, showing that in some Berger spheres (a… Expand

New examples of constant mean curvature surfaces in S^2xR and H^2xR

- J. M. Manzano, Francisco Torralbo
- Mathematics
- 7 April 2011

We construct non-zero constant mean curvature H surfaces in the product spaces $\mathbb{S}^2 \times \mathbb{R}$ and $\mathbb{H}^2\times \mathbb{R}$ by using suitable conjugate Plateau constructions.… Expand

Parallel mean curvature surfaces in four-dimensional homogeneous spaces

- J. M. Manzano, Francisco Torralbo, J. Veken
- Mathematics, Physics
- 13 January 2017

We survey different classification results for surfaces with parallel mean curvature immersed into some Riemannian homogeneous four-manifolds, including real and complex space forms, and product… Expand

Minimal Surfaces in $\mathbb{S}^{2} \times\mathbb{S}^{2}$

- Francisco Torralbo, F. Urbano
- Mathematics
- 2015

A general study of minimal surfaces of the Riemannian product of two spheres $\mathbb {S}^{2}\times \mathbb {S}^{2}$ is tackled. We establish a local correspondence between (non-complex) minimal… Expand

Compact embedded minimal surfaces in $\mathbb{S}^2\times \mathbb{S}^1$

- J. M. Manzano, Julia Plehnert, Francisco Torralbo
- Mathematics
- 11 November 2013

We prove that closed surfaces of all topological types, except for the non-orientable odd-genus ones, can be minimally embedded in the Riemannian product of a sphere and a circle of arbitrary radius.… Expand

A geometrical correspondence between maximal surfaces in anti-De Sitter space–time and minimal surfaces in H2×R

- Francisco Torralbo
- Mathematics
- 15 March 2015

Abstract A geometrical correspondence between maximal surfaces in anti-De Sitter space–time and minimal surfaces in the Riemannian product of the hyperbolic plane and the real line is established.… Expand

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