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

Rami Younes

arXiv:1002.4647·math.DG·February 26, 2010·1 cites

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

Rami Younes

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Abstract

We study minimal graphs in the homogeneous Riemannian 3-manifold $P S L_{2} (R)$ 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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TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology