Laguerre minimal surfaces in ?3

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 ℝ₀³. This work is supported by RFDP (No. 20040001034)