Illinois Journal of Mathematics

Minimal surfaces in $\widetilde{\mathit{PSL}_{2}(\mathbb{R})}$

Rami Younes

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Abstract

We study minimal graphs in the homogeneous Riemannian 3-manifold $\widetilde{\mathit{PSL}_{2}(\mathbb{R})}$ 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.

Article information

Source
Illinois J. Math., Volume 54, Number 2 (2010), 671-712.

Dates
First available in Project Euclid: 14 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1318598677

Digital Object Identifier
doi:10.1215/ijm/1318598677

Mathematical Reviews number (MathSciNet)
MR2846478

Zentralblatt MATH identifier
1235.53064

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

Citation

Younes, Rami. Minimal surfaces in $\widetilde{\mathit{PSL}_{2}(\mathbb{R})}$. Illinois J. Math. 54 (2010), no. 2, 671--712. doi:10.1215/ijm/1318598677. https://projecteuclid.org/euclid.ijm/1318598677


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