  We consider on Riemannian manifolds the nonlinear evolution equation
\begin{equation*} \partial _{t}u=\Delta _{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 $\mathbb{R}^{n}$.
