Pincement du plan hyperbolique complexe

Pierre Pansu (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

$L^p$-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 $-\frac{1}{4}$-pinched sectional curvature can be quasiisometric to complex hyperbolic plane. Unfortunately, the method does not extend to other rank one symmetric spaces.

Mots clés: $L^{p}$-cohomology; negative curvature; symmetric space; Besov space; Royden algebra

Domaines: Géométrie différentielle [math.DG]; Géométrie métrique [math.MG]

Pierre Pansu. Pincement du plan hyperbolique complexe. 2009. ⟨hal-00579013⟩