A fundamental solution for a subelliptic operator in Finsler geometry

We introduce a class of nonlinear partial differential equations in a product space which are at the interface of Finsler and sub-Riemannian geometry. With such equations we associate a non-isotropic Minkowski gauge Θ for which we introduce a suitable notion of Legendre transform Θ0. We compute the action of the relevant nonlinear PDEs on “radial” func-tions, that is, functions of Θ0, and by exploiting it we are able to compute explicit fundamental solutions of such PDEs.