Open manifolds with nonnegative Ricci curvature and large volume growth | Zendy

Changyu Xia | Zendy

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Open manifolds with nonnegative Ricci curvature and large volume growth

Author(s) -

Changyu Xia

Publication year - 1999

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140050099

Subject(s) - mathematics , ricci curvature , sectional curvature , minimal volume , riemannian manifold , manifold (fluid mechanics) , pure mathematics , geodesic , curvature , scalar curvature , bounded function , diffeomorphism , euclidean space , curvature of riemannian manifolds , volume (thermodynamics) , ricci flat manifold , mathematical analysis , geometry , physics , mechanical engineering , quantum mechanics , engineering

In this paper,we prove that a complete n-dimensional Riemannian manifold with n0nnegative kth-Ricci curvature,large volume growth has finite topological type provided that lim{((vol[B(p,r))]/(ω_nr~n)-αM)r(k(n-1))/(k+1)(1-α/2)}=εfor some constantε0.We also prove that a complete Riemannian manifold with nonnegative kth-Ricci curvature and under some pinching conditions is diffeomorphic to R~n.

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