Constant Mean Curvature Surfaces in Hyperbolic Space

López, Rafael

doi:10.1007/978-3-642-39626-7_10

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Cited by 2 publications

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“…• Replace the ambient space R n+1 by the hyperbolic spaces H n+1 [4,18,24,29] or other ambient spaces with a Killing field satisfying certain hypotheses [1,11,12]. In this setting it is natural to consider CMC Killing graphs and there is an extensive bibliography on it.…”

Section: Introductionmentioning

confidence: 99%

A note on minimal graphs over certain unbounded domains of Hadamard manifolds

Telichevesky

2016

Pacific J. Math.

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Given an unbounded domain Ω of a Hadamard manifold M , it makes sense to consider the problem of finding minimal graphs with prescribed continuous data on its cone-topology-boundary, i.e., on its ordinary boundary together with its asymptotic boundary. In this article it is proved that under the hypothesis that the sectional curvature of M is ≤ −1 this Dirichlet problem is solvable if Ω satisfies certain convexity condition at infinity and if ∂Ω is mean convex. We also prove that mean convexity of ∂Ω is a necessary condition, extending to unbounded domains some results that are valid on bounded ones.

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Section: Introductionmentioning

confidence: 99%

A note on minimal graphs over certain unbounded domains of Hadamard manifolds

Telichevesky

2016

Pacific J. Math.

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“…In [12], Lopez studied a parabolic surface in hyperbolic space H 3 is a surface invariant by a group of parabolic isometries, then, describe all parabolic surfaces with constant Gaussian curvature. In [13], Lopez gave a space-like or time-like surface in Lorentz-Minkowski three-space L 3 generated by a oneparameter family of circular arcs and later, he obtain if the Gauss curvature K is a nonzero constant, then M is a surface of revolution. We also describe the parametrizations for M when K ≡ 0.…”

Section: Introductionmentioning

confidence: 99%