Article Dans Une Revue Année : 2017

Discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3 : a discrete Lawson correspondence

Résumé

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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Dates et versions

hal-01517411 , version 1 (03-05-2017)
hal-01517411 , version 2 (05-10-2017)

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Alexander I Bobenko, Pascal Romon. Discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3 : a discrete Lawson correspondence. 2017, 2 (1), pp.1-18. ⟨10.1093/integr/xyx010⟩. ⟨hal-01517411v1⟩
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