Calibrations and isoperimetric profiles

We equip many non compact non simply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly non generic property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, together with new results on the profile of surfaces of revolution and some hardware know-how.Comment: To appear soon in American Journal of Mathematics, a journal published by The Johns Hopkins University Pres

Density of Zariski density for surface groups

We show that a surface group contained in a reductive real algebraic group can be deformed to become Zariski dense, unless its Zariski closure acts transitively on a Hermitian symmetric space of tube type. This is a kind of converse to a rigidity result of Burger, Iozzi and Wienhard

Averages and the ℓq,1\ell^{q,1}-cohomology of Heisenberg groups

Averages are invariants defined on the $\ell^1$ cohomology of Lie groups. We prove that they vanish for abelian and Heisenberg groups. This result completes work by other authors and allows to show that the $\ell^1$ cohomology vanishes in these cases

Bounded geometry, growth and topology

We characterize functions which are growth types of Riemannian manifolds of bounded geometry.Comment: 15 page