Pincement du plan hyperbolique complexe

Publication date: 23 March 2011

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.

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