Year: 2010
Type: article
Abstract: . We give an overview on the discretization of isothermic surfaces, with special emphasis on the so-called s-isothermic surfaces, which are in some sense a nonlinear deformation of the classical discrete isothermic surfaces. For s-isothermic surfaces we give a way to define surfaces of constant mean curvature (cmc surfaces for short) without actually defining an a priori notion of curvature itself. We will compute discrete versions of rotational symmetric cmc surfaces (Delaunay surfaces) as an example. Finally, we give a discrete equivalent of the Sinh-Gordon equation, solutions of which describe – in complete analogy to the smooth case – discrete s-isothermic cmc surfaces.
Author: Tim Hoffmann
Institution: Technical University of Munich
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W233538280