Bootstrapping closed hyperbolic surfaces

A bstract The eigenvalues of the Laplace-Beltrami operator and integrals products eigenfunctions holomorphic s -differentials satisfy certain consistency conditions on closed hyperbolic surfaces. These can be derived by using spectral decompositions to write quadruple overlap in terms triple different ways. We show how efficiently construct these use them derive upper bounds eigenvalues, following approach conformal bootstrap. As an example such a bootstrap bound, we find numerical bound gap orientable surfaces that is nearly saturated Bolza surface.