Improved critical eigenfunction estimates on manifolds of nonpositive curvature
Improved critical eigenfunction estimates on manifolds of nonpositive curvature
We prove new improved endpoint, $L^{p_c}$, $p_c=\tfrac{2(n+1)}{n-1}$, estimates (the kink point) for eigenfunctions on manifolds of nonpositive curvature. We do this by using energy and dispersive estimates for the wave equation as well as new improved $L^p$, $2<p< p_c$, bounds of Blair and the author \cite{BSTop}, \cite{BSK15} and the classical …