Regularity for a class of quasilinear degenerate parabolic equations in the Heisenberg group

We extend to the parabolic setting some of ideas originated with Xiao Zhong's proof in [31] Hölder regularity $p-$harmonic functions Heisenberg group $\mathbb{H}^n$. Given a number $p\ge 2$, this paper we establish $C^{\infty}$ smoothness weak solutions class quasilinear PDE $\mathbb{H}^n$ modeled on equation $$?_t u = \sum_{i 1}^{2n} X_i \bigg((1+|\nabla_0 u|^2)^{\frac{p-2}{2}} u\bigg).$$