Pincement du plan hyperbolique complexe

Abstract

$L^p$-cohomology of rank one symmetric spaces of noncompact type is shown to be Hausdorff for values of $p$ where this does not follow from curvature pinching. Using the multiplicative structure on $L^p$-cohomology, it is shown that no simply connected Riemannian manifold with strictly -1/4-pinched sectional curvature can be quasiisometric to complex hyperbolic plane. Unfortunately, the method does not extend to other rank one symmetric spaces.

39 pages. Manuscript completed in january 2009, with a minor change last fall. Missing: careful proof of quasiisometry invariance of cup-product in L^p cohomology, postponed to a separate paper