An $\ell_1$-norm-mass inequality for complete manifolds

Caterina Campagnolo, Shi Wang

Published 2022-03-08Version 1

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.