An ${\ell }_1$-norm-mass inequality for complete manifolds

Abstract

We generalize an inequality of Besson-Courtois-Gallot about volume and simplicial volume of closed manifolds to the ${\ell }_1$-norm of all the homology classes of complete manifolds. The inequality involves the critical exponent of the fundamental group of the manifold and the mass of the homology classes.

16 pages. Final version, to appear at Annales de l'Institut Fourier