Critical exponent and bottom of the spectrum in pinched negative curvature
Critical exponent and bottom of the spectrum in pinched negative curvature
In this note, we present a new proof of the celebrated theorem of Patterson-Sullivan which relates the critical exponent of a hyperbolic manifold and the bottom of its spectrum.The proof extends to manifolds with pinched negative curvatures.It provides a sufficient criterion for the existence of isolated eigenvalues for the Laplacian …