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Journal of the London Mathematical Society 2005 72(1):258-272; doi:10.1112/S0024610705006472
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© The London Mathematical Society

Constant Mean Curvature Surfaces of any Positive Genus

M. Kilian, S.-P. Kobayashi, W. Rossman and N. Schmitt

Mathematical Sciences, University of Bath Bath BA2 7AY, United Kingdom masmk{at}maths.bath.ac.uk
Department of Mathematics, Kobe University Rokko Kobe 657-8501, Japan kobayasi{at}math.kobe-u.ac.jp, wayne{at}math.kobe-u.ac.jp
Institut für Mathematik, Technische Universität Berlin Straße des 17 Juni 136, 10623 Berlin, Germany nick{at}gang.umass.edu

Received 17 March 2004.

The paper shows the existence of several new families of noncompact constant mean curvature surfaces: (i) singly punctured surfaces of arbitrary genus g≥1, (ii) doubly punctured tori, and (iii) doubly periodic surfaces with Delaunay ends.


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