2 problems

Let $M$ be a Riemannian manifold, and let $P_+$ and $P_0$ be respectively subcritical and critical operators in $M$. Critical-subcritical decay conjecture. The ratio … locally unif…

Let $Lu=u_t+P(x,\partial_x)u$ be a parabolic operator defined on a noncompact Riemannian manifold $M$, with $\lambda_0(P,M)\geq 0$. Fix a reference point $x_0\in M$. Davies' conjec…