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