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M. Magdalena Rodríguez

Publications and source records attributed to M. Magdalena Rodríguez.

5 recordsLinked to original sources
arXiv2012

On complete constant mean curvature vertical multigraphs in E(κ,τ)

We prove that any complete surface with constant mean curvature in a homogeneous space E(κ,τ) which is transversal to the vertical Killing vector field is, in fact, a vertical graph. As a consequence we get that any orientable, parabolic, complete, immersed surface with constant mean curvature H in E(κ,τ) (different from a horizontal slice in S^2xR) is either a vertical cylinder or a vertical graph (in both cases, it must be 4H^2+κ\leq0).

math.DG↗
arXiv2011

Minimal surfaces with limit ends in H^2 x R

For any m > 0, we construct properly embedded minimal surfaces in H^2 x R with genus zero, infinitely many vertical planar ends and m limit ends. We also provide examples with an infinite countable number of limit ends. All these examples are vertical bi-graphs.

math.DG↗
arXiv2011

Periodic constant mean curvature surfaces in H^2 x R

In this paper we study minimal and constant mean curvature (cmc) periodic surfaces in H^2 x R. More precisely, we consider quotients of H^2 x R by discrete groups of isometries generated by horizontal hyperbolic translations f and/or a vertical translation T. In the quotient by the Z^2 subgroup of the isometry group generated by any f and T, we prove an Alexandrov-type theorem for cmc surfaces, i.e., an analysis of compact embedded cmc surfaces in such a quotient. The remainder of the paper is devoted to construct examples of periodic minimal surfaces in H^2 x R.

math.DG↗
arXiv2011

Non-simply connected minimal planar domains in H^2 x R

We prove that any non-simply connected planar domain can be properly and minimally embedded in H^2 x R. The examples that we produce are vertical bi-graphs, and they are obtained from the conjugate surface of a Jenkins-Serrin graph.

math.DG↗