Pincement du plan hyperbolique complexe

2011/03/23 by Pierre Pansu, Pansu, Pierre
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1103.4460

openalex publication_date 2011/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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