Pincement du plan hyperbolique complexe

Details Pincement du plan hyperbolique complexe Pincement du plan hyperbolique complexe

2011-03-23

arxiv.org/abs/1103.4460v1

Mathematics

Differential Geometry

39 pages. Manuscript completed in january 2009, with a minor change last fall. Missing: careful proof of quasiisometry invaria

Scientific paper

$L^p$-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.

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