Existence and uniqueness for the parabolic infinite-Laplace Cauchy-Dirichlet problem

Let $\Omega$ be a bounded domain in a Carnot group and let $T>0$. Let $\psi\in C(\overline{\Omega})$ and $g\in C(\Omega\times[0,T))$. The Cauchy-Dirichlet problem

$$\left\{ \begin{array}{cl} u_t-\Delta^h_{\infty}u=0&\text{in }\Omega\times(0,T),\\ u(x,0)=\psi(x)&\text{on }\overline{\Omega},\\ u(x,t)=g(x,t)&\text{on }\partial\Omega\times(0,T) \end{array} \right.$$

Existence and uniqueness claim. The problem has a unique viscosity solution $u$.

The paper presents this as the parabolic analogue of the established elliptic infinite-Laplace Dirichlet problem in Carnot groups; the stated result concerns existence and uniqueness for the specified class of parabolic equations.