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arXiv · 1712.08564

Minimal surfaces from infinitesimal deformations of circle packings

Wai Yeung Lam
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Abstract

We study circle packings with the combinatorics of a triangulated disk in the plane and parametrize deformations of circle packings in terms of vertex rotation and cross ratios. We show that there is a Weierstrass representation formula relating infinitesimal deformations of circle packings to discrete minimal surfaces of Koebe type. Furthermore, every minimal surface of Koebe type can be extended naturally to a discrete minimal surface of general type. In this way, discrete minimal surfaces via Steiner's formula are unified.

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Wai Yeung Lam. 2017-12-22. Minimal surfaces from infinitesimal deformations of circle packings. https://arxiv.org/abs/1712.08564

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