An inequality between complex Hessian measures of Holder continuous m-subharmonic functions and capacity

Abstract

For a Riemannian covering π : M1 → M0, the bottoms of the spectra of M0 and M1 coincide if the covering is amenable. The converse implication does not always hold. Assuming completeness and a lower bound on the Ricci curvature, we obtain a converse under a natural condition on the spectrum of M0.