An l_1-norm inequality for complete manifolds
20.30 SR 2.058
Proved in the 80's, Gromov's "Main inequality" is one of the prominent results about simplicial volume of manifolds: it relates the simplicial volume, a topological invariant, to the volume of the manifold, a geometric quantity, under some curvature assumptions.
The community has tried to generalize and enhance Gromov's result by weakening the curvature assumptions, extending, or improving the inequality.
In joint work with Shi Wang, we extend the results of Besson-Courtois-Gallot about the l_1-norm of the fundamental class of a closed manifold to all homology classes of a complete manifold. Our inequalities are sharper than Gromov's original ones and are expressed in terms of the critical exponent of the manifold.
I will define the necessary objects, give some context and the main ideas of the proof.