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Laguerre minimal surfaces in ℝ3

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Abstract

Laguerre geometry of surfaces in ℝ3 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 ℝ3. We show that any Laguerre minimal surface in ℝ3 can be constructed by using at most two holomorphic functions. We show also that any Laguerre minimal surface in ℝ3 with constant Laguerre curvature is Laguerre equivalent to a surface with vanishing mean curvature in the 3-dimensional degenerate space ℝ 30 .

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Authors and Affiliations

  1. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China

    Yu Ping Song & Chang Ping Wang

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  1. Yu Ping Song
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  2. Chang Ping Wang
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Correspondence to Yu Ping Song.

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This work is supported by RFDP (No. 20040001034)

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Song, Y.P., Wang, C.P. Laguerre minimal surfaces in ℝ3 . Acta. Math. Sin.-English Ser. 24, 1861–1870 (2008). https://doi.org/10.1007/s10114-008-7117-0

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  • DOI: https://doi.org/10.1007/s10114-008-7117-0

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