Minimal surfaces and harmonic diffeomorphisms from the complex plane onto a Hadamard surface

Details Minimal surfaces and harmonic diffeomorphisms from the complex plane onto a Hadamard surface Minimal surfaces and harmonic diffeomorphisms from the complex plane onto a Hadamard surface

2008-07-07

arxiv.org/abs/0807.0997v1

Mathematics

Differential Geometry

23 pages, 10 figures

Scientific paper

We construct harmonic diffeomorphisms from the complex plane $C$ onto any Hadamard surface $M$ whose curvature is bounded above by a negative constant. For that, we prove a Jenkins-Serrin type theorem for minimal graphs in $M\times R$ over domains of $M$ bounded by ideal geodesic polygons and show the existence of a sequence of minimal graphs over polygonal domains converging to an entire minimal graph in $M\times R$ with the conformal structure of $C$.

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