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BIBTEX RIS

Lipschitz convergence of Riemannian manifolds

1988; Mathematical Sciences Publishers; Volume: 131; Issue: 1 Linguagem: Inglês

10.2140/pjm.1988.131.119

ISSN

1945-5844

Autores

Robert E. Greene, Hung-Hsi Wu,

Tópico(s)

Advanced Banach Space Theory

Resumo

Let #s <g(n,A,8 O9 V o ) be the set of all connected compact C°°dimensional Riemannian manifolds with |sectional curvature | < Λ 2 , diameter < 8 0 , and volume > V o .The main result of this paper is that this class ^ has certain compactness, or more precisely, precompactness properties.The class # consists of only finitely many diffeomorphism classes so the precompactness properties can be thought of as dealing with the set of metrics satisfying the class # requirements on a fixed differentiate manifold.The main theorem of this paper is then that a sequence of such metrics always has a subsequence which, after application of suitable diffeomorphisms of M, converges to a limit metric.The regularity of the limit can be taken to be C lα , for all a with 0 < a < 1 and the convergence to be in the C ι ' a norm.

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