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.

arXiv comment39 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

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