On a Bernstein-type theorem for minimal surfaces with Matsumoto metric

In this paper we characterize a minimal surface with Matsumoto metric and prove a Bernstein-type theorem for surfaces which are graphs of smooth functions. We also obtain the partial differential equation that characterizes the minimal translation surfaces and show that plane is the only such surface.

Keywords:

Finsler spaces , Matsumoto metric , Minimal surfaces , Graph of a function , Surface of translation