Discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. A discrete Lawson correspondence

Alexander I. Bobenko; Pascal Romon

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arXiv · 1705.01053

Discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. A discrete Lawson correspondence

Alexander I. Bobenko·Pascal Romon

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Abstract

The main result of this paper is a discrete Lawson correspondence between discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. This is a correspondence between two discrete isothermic surfaces. We show that this correspondence is an isometry in the following sense: it preserves the metric coefficients introduced previously by Bobenko and Suris for isothermic nets. Exactly as in the smooth case, this is a correspondence between nets with the same Lax matrices, and the immersion formulas also coincide with the smooth case.

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Alexander I. Bobenko, Pascal Romon. 2017-05-02. Discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. A discrete Lawson correspondence. https://arxiv.org/abs/1705.01053

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