#### Volume 18, issue 1 (2014)

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

### Francisco Martín, Rafe Mazzeo and M Magdalena Rodríguez

Geometry & Topology 18 (2014) 141–177
##### Abstract

We construct the first examples of complete, properly embedded minimal surfaces in ${ℍ}^{2}×ℝ$ 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.

##### Keywords
properly embedded minimal surfaces, finite total curvature, gluing constructions, moduli spaces, minimal surfaces, positive genus
##### Mathematical Subject Classification 2010
Primary: 49Q05, 53A10, 53C42