| Laguerre minimal surfaces in ℝ3 |
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| 基金项目： | This work is supported by RFDP （No. 20040001034）Acknowledgment Part of the results are obtained during the visit of the second author at TU Berlin. He would like to thank Pinkall and Simon for their hospitality, and thank Bobenko for references to the Liouville equation. |
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| 摘 要： | Laguerre geometry of surfaces in R^3 is given in the book of Blaschke, and has been studied by Musso and Nicolodi, Palmer, Li and Wang and other authors. In this paper we study Laguerre minimal surface in 3-dimensional Euclidean space R^3. We show that any Laguerre minimal surface in R^3 can be constructed by using at most two holomorphic functions. We show also that any Laguerre minimal surface in R^3 with constant Laguerre curvature is Laguerre equivalent to a surface with vanishing mean curvature in the 3-dimensional degenerate space R0^3.
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| 关 键 词： | 几何学 最小平面 高斯映射 欧几里得空间 |
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