# \(L^p\)-cohomology and pinching

### (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.