Volume 18, issue 1 (2014)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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 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.

Keywords
properly embedded minimal surfaces, finite total curvature, gluing constructions, moduli spaces, minimal surfaces, positive genus
Mathematical Subject Classification 2010
Primary: 49Q05, 53A10, 53C42
References
Publication
Received: 30 August 2012
Revised: 6 May 2013
Accepted: 19 July 2013
Preview posted: 5 December 2014
Published: 9 January 2014
Proposed: Tobias H Colding
Seconded: David Gabai, Ronald Stern
Authors
Francisco Martín
Departamento de Geometría y Topología
Universidad de Granada
18071 Granada
Spain
http://www.ugr.es/local/fmartin
Rafe Mazzeo
Department of Mathematics
Stanford University
Stanford, CA 94305
USA
http://math.stanford.edu/~mazzeo/
M Magdalena Rodríguez
Departamento de Geometría y Topología
Universidad de Granada
18071 Granada
Spain
http://www.ugr.es/local/magdarp