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Rotationally invariant constant mean curvature surfaces in homogeneous 3-manifolds
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 constantExpand
Compact minimal surfaces in the Berger spheres
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 areExpand
On stable compact minimal submanifolds
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 theExpand
Compact stable constant mean curvature surfaces in homogeneous 3-manifolds
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 areExpand
Compact stable constant mean curvature surfaces in the Berger spheres
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 (aExpand
New examples of constant mean curvature surfaces in S^2xR and H^2xR
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
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 productExpand
Minimal Surfaces in $\mathbb{S}^{2} \times\mathbb{S}^{2}$
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) minimalExpand
Compact embedded minimal surfaces in $\mathbb{S}^2\times \mathbb{S}^1$
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
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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