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Minimal surfaces with positive genus and finite total curvature in $$\mathbb{H}^2 \times \mathbb{R}$$. (English) Zbl 1280.49062
Summary: We construct the first examples of complete, properly embedded minimal surfaces in $$\mathbb{H}^2 \times \mathbb{R}$$ 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.

##### MSC:
 49Q05 Minimal surfaces and optimization 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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