Weierstrass representations of Laguerre minimal surfaces in R-3

Let x : M -> R-3 be an oriented surface with non-zero Gauss curvature K and mean curvature H. The functional L(x) = integral(M)(H-2 - K)/K dM is invariant under a 10 dimensional group, called Laguerre group, which includes the isometry group of R3 as subgroup. The critical surfaces of L are called Laguerre minimal surfaces. In this paper we give a method to construct all Laguerre minimal surfaces locally by using one holomorphic function and two meromorphic functions.Mathematics, AppliedMathematicsSCI(E)10ARTICLE3-4399-4085