Isothermic triangulated surfaces
Abstract
We found a class of triangulated surfaces in Euclidean space which have similar properties as isothermic surfaces in Differential Geometry. We call a surface isothermic if it admits an infinitesimal isometric deformation preserving the mean curvature integrand locally. We show that this class is M\"{o}bius invariant. Isothermic triangulated surfaces can be characterized either in terms of circle patterns or based on conformal equivalence of triangle meshes. This definition generalizes isothermic quadrilateral meshes. A consequence is a discrete analog of minimal surfaces. Here the Weierstrass data needed to construct a discrete minimal surface consist of a triangulated plane domain and a discrete harmonic function.
Cite
@article{arxiv.1501.02587,
title = {Isothermic triangulated surfaces},
author = {Wai Yeung Lam and Ulrich Pinkall},
journal= {arXiv preprint arXiv:1501.02587},
year = {2016}
}
Comments
29 pages, 7 figures; v2: references added, typos corrected and minor changes; v3: section 1-2,8-11 revised and references added; v4: minor changes