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2014 Minimal surfaces with positive genus and finite total curvature in $\mathbb{H}^2 \times \mathbb{R}$
Francisco Martín, Rafe Mazzeo, M Magdalena Rodríguez
Geom. Topol. 18(1): 141-177 (2014). DOI: 10.2140/gt.2014.18.141

Abstract

We construct the first examples of complete, properly embedded minimal surfaces in 2× with finite total curvature and positive genus. These are constructed by gluing copies of horizontal catenoids or other nondegenerate summands. We also establish that every horizontal catenoid is nondegenerate.

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Francisco Martín. Rafe Mazzeo. M Magdalena Rodríguez. "Minimal surfaces with positive genus and finite total curvature in $\mathbb{H}^2 \times \mathbb{R}$." Geom. Topol. 18 (1) 141 - 177, 2014. https://doi.org/10.2140/gt.2014.18.141

Information

Received: 30 August 2012; Revised: 6 May 2013; Accepted: 19 July 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1280.49062
MathSciNet: MR3158774
Digital Object Identifier: 10.2140/gt.2014.18.141

Subjects:
Primary: 49Q05, 53A10, 53C42

Rights: Copyright © 2014 Mathematical Sciences Publishers

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