Minimal surfaces of rotation in Finsler space with a Randers metric

We consider Finsler spaces with a Randers metric F alpha + beta, on the three dimensional real vector space, where alpha is the Euclidean metric and beta = bdx(3) is a 1-form with norm b, 0 less than or equal to b < 1. By using the notion of mean curvature for immersions in Finsler spaces introduced by Z. Shen, we get the ordinary differential equation that characterizes the minimal surfaces of rotation around the x(3) axis. We prove that for every b, 0 less than or equal to b < 1, there exists, up to homothety, a unique forward complete minimal surface of rotation. The surface is embedded, symmetric with respect to a plane perpendicular to the rotation axis and it is generated by a concave plane curve. Moreover, for every b, root3/3 < b < 1 there are non complete minimal surfaces of rotation, which include explicit minimal cones.