Atlas home || Conferences | Abstracts | about Atlas

Geometry and Applications
March 13-16, 2000
Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences and Novosibirsk State University
Novosibirsk, Russia

Organizers
Yu.G. Rushetnyak (Chair of Program Committee; Russia), V.V. Vershinin (Chair of Organizing Committee; Russia), A.A. Borisenko (Ukraine), Yu.D. Burago (Russia), V.M. Gol'dshtein (Israel), M.L. Gromov (France), I.G. Nikolaev (USA/Russia), S.P. Novikov (USA/Russia), A.V. Pogorelov (Ukraine), I.Kh. Sabitov (Russia)

View Abstracts
Conference Homepage

Discrete Conjugate Minimal Surfaces
by
Konrad Polthier
Fachbereich Mathematik, Technische Universitaet Berlin

We consider discrete harmonic maps that are conforming or non-conforming piecewise linear maps, and derive a bijection between the minimizers of the two corresponding Dirichlet problems. Pairs of harmonic maps with a conforming and a non-conforming component solve the discrete Cauchy-Riemann equations, and have vanishing discrete conformal energy.

As an application, the results of this work provide a thorough understanding of the conjugation algorithms of Pinkall/Polthier and Oberknapp/Polthier used in the computation of discrete minimal and constant mean curvature surfaces.

Date received: January 18, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadw-03.