Mathematische Zeitschrift

, Volume 279, Issue 1–2, pp 459–478 | Cite as

Semi-discrete constant mean curvature surfaces

Article

Abstract

We study semi-discrete surfaces in three dimensional euclidean space which are defined on a parameter domain consisting of one smooth and one discrete parameter. More precisely, we consider only those surfaces which are glued together from individual developable surface strips. In particular we investigate minimal surfaces and constant mean curvature (CMC) surfaces with non vanishing mean curvature in the setting of Koenigs nets and Christoffel duality. We obtain incidence-geometric characterizations of the dualizability of Koenigs nets as well as for the Gauss image of CMC surfaces. We also consider isothermic semi-discrete CMC surfaces and a specific type of Cauchy problem in this regard.

Keywords

Discrete differential geometry Semi-discrete surfaces  Minimal surfaces CMC surfaces 

Mathematics Subject Classification

39A12 53A05 53A10 53A40 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute of Discrete Mathematics and GeometryVienna University of TechnologyViennaAustria

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