Discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. A discrete Lawson correspondence
Discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. A discrete Lawson correspondence
复制标题
R^3 中的离散 CMC 曲面和 S^3 中的离散最小曲面。
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
P. Romon
中科院分区：
文献类型：
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作者：
A. Bobenko;P. Romon
本文的主要结果是R^3中离散CMC曲面与S^3中离散极小曲面之间的离散Lawson对应。这是两个离散等温曲面之间的对应。我们证明了这种对应在以下意义上是等距的：它保持了Bobenko和Suris先前为等温网引入的度量系数。与光滑情形完全一样，这是具有相同Lax矩阵的网之间的对应，并且浸没公式也与光滑情形一致。
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.