Geometry & Topology

Minimal surfaces with positive genus and finite total curvature in $\mathbb{H}^2 \times \mathbb{R}$

Francisco Martín, Rafe Mazzeo, and M Magdalena Rodríguez

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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.

Article information

Geom. Topol., Volume 18, Number 1 (2014), 141-177.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49Q05: Minimal surfaces [See also 53A10, 58E12] 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

properly embedded minimal surfaces finite total curvature gluing constructions moduli spaces minimal surfaces positive genus


Martín, Francisco; Mazzeo, Rafe; Rodríguez, M Magdalena. Minimal surfaces with positive genus and finite total curvature in $\mathbb{H}^2 \times \mathbb{R}$. Geom. Topol. 18 (2014), no. 1, 141--177. doi:10.2140/gt.2014.18.141.

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