Minimal surfaces in non-Minkowskian Randers spaces

In this paper, we investigate minimal hypersurfaces in Rⁿ with respect to the Busemann--Hausdorff measure in a class of Finsler n-spaces (Rⁿ,F̃b=α̃+β̃), called Randers spaces, where α̃ is the Euclidean metric and β̃=b(x)dyⁿ is a controlled one-form. We emphasize the fact that F is non-Minkowskian, since $b=b(x)$ is a non-constant function of x, which is allowed here. We particularly examine graphs defined on the $xy$-plane that are invariant under one-dimensional isometry groups of (R³,F̃b). By reducing the minimal graph equation to an ordinary differential equation (ODE), we obtain a new class of explicit examples of minimal surfaces in Finsler geometry.