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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 446
Conjugate Harmonic Maps and Minimal Surfaces Konrad Polthier
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.
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