L p -Cohomology and Pinching

Pierre Pansu ()
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Pierre Pansu: Université Paris-Sud, UMR 8628 du CNRS, Laboratoire de Mathématiques, Equipe de Topologie et Dynamique

A chapter in Rigidity in Dynamics and Geometry, 2002, pp 379-389 from Springer

Abstract: Abstract This paper is an exposition of some material from [P]. We explain how torsion in L p -cohomology can be used to prove a sharp pinching theorem for simply connected Riemannian manifolds with negative curvature. Namely, it is shown that a certain Riemannian homogeneous space whose curvature is negative and ¼-pinched cannot be quasi-isometric to any Riemannian manifold whose curvature is less than ¼-pinched.

Keywords: Riemannian Manifold; Symmetric Space; Besov Space; Ideal Boundary; Poincare Duality (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04743-9_20

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DOI: 10.1007/978-3-662-04743-9_20

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