Endpoint resolvent estimates for compact Riemannian manifolds

Rupert L. Frank, Lukas Schimmer

We prove $L^p\to L^{p^{\prime }}$ bounds for the resolvent of the Laplace-Beltrami operator on a compact Riemannian manifold of dimension $n$ in the endpoint case $p=2(n+1)/(n+3)$. It has t…