\(L^p\)-cohomology and pinching

Pierre Pansu

(Université Paris-Sud)

Event: ERC Workshop on Geometric Analysis on sub-Riemannian and Metric Spaces

Date: Oct 12, 2011, time: 08:30

Place: Centro De Giorgi, Scuola Normale Superiore

Abstract. We prove that Riemannian manifolds quasiisometric to complex hyperbolic plane cannot have sectional curvature pinched between \(-1\) and a for \(a<-\frac{1}{4}\). The proof uses the multiplicative structure on \(L^p\)-cohomology and considerations on differential forms on the Heisenberg group.