Minimal Surfaces in $\widetilde{PSL_2(\mathbb{R})}$

Details Minimal Surfaces in $\widetilde{PSL_2(\mathbb{R})}$ Minimal Surfaces in $\widetilde{PSL_2(\mathbb{R})}$

2010-02-24

arxiv.org/abs/1002.4647v1

Mathematics

Differential Geometry

47 pages, 0 figures. To be published in Illinois Journal of Mathematics

Scientific paper

We study minimal graphs in the homogeneous Riemannian 3-manifold
$\widetilde{PSL_2(\mathbb{R})}$ and we give examples of invariant surfaces. We
derive a gradient estimate for solutions of the minimal surface equation in
this space and develop the machinery necessary to prove a Jenkins-Serrin type
theorem for solutions defined over bounded domains of the hyperbolic plane.

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