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

Rami Younes

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

Differential Geometry 2010-02-26 v1

Authors: Rami Younes

Abstract

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.

Keywords

minimal surfaces surface theory hyperbolic surfaces

Cite

@article{arxiv.1002.4647,
  title  = {Minimal Surfaces in $\widetilde{PSL_2(\mathbb{R})}$},
  author = {Rami Younes},
  journal= {arXiv preprint arXiv:1002.4647},
  year   = {2010}
}

Comments

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

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