Sharp sub-Gaussian upper bounds for subsolutions of Trudinger's equation on Riemannian manifolds

We consider on Riemannian manifolds the nonlinear evolution equation \begin{equation*} \partial {t}u=Δ{p}(u^{1/(p-1)}), \end{equation*}% where $p>1$. This equation is also known as a doubly non-linear parabolic equation or Trudinger’s equation. We prove that weak subsolutions of this equation have a sub-Gaussian upper bound and prove that this upper bound is sharp for a specific class of manifolds including ${\mathbb{R}}^n$.