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

We consider on Riemannian manifolds the nonlinear evolution equation ∂tu=Δp(u1/(p−1)),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 Rn.