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Minimal surfaces and harmonic diffeomorphisms from the complex plane onto certain Hadamard surfaces
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 132, Number 5, October 2010
- pp. 1249-1273
- 10.1353/ajm.2010.0001
- Article
- Additional Information
We construct harmonic diffeomorphisms from the complex plane ${\bf C}$
onto any Hadamard surface $\mathbb{M}$ whose curvature is bounded above by
a negative constant. For that, we prove a Jenkins-Serrin type theorem for
minimal graphs in $\mathbb{M} \times \mathbb{R}$ over domains of
$\mathbb{M}$ 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 $\mathbb{M} \times \mathbb{R}$ with the conformal
structure of ${\bf C}$.