Duke Mathematical Journal

Gap theorems for noncompact Riemannian manifolds

R. E. Greene and H. Wu

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Article information

Source
Duke Math. J., Volume 49, Number 3 (1982), 731-756.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077315386

Digital Object Identifier
doi:10.1215/S0012-7094-82-04937-7

Mathematical Reviews number (MathSciNet)
MR672504

Zentralblatt MATH identifier
0513.53045

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]

Citation

Greene, R. E.; Wu, H. Gap theorems for noncompact Riemannian manifolds. Duke Math. J. 49 (1982), no. 3, 731--756. doi:10.1215/S0012-7094-82-04937-7. https://projecteuclid.org/euclid.dmj/1077315386


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References

  • [AW] C. B. Allendoerfer and A. Weil, The Gauss-Bonnet theorem for Riemannian polyhedra, Trans. Amer. Math. Soc. 53 (1943), 101–129.
  • [BC] R. L. Bishop and R. J. Crittenden, Geometry of manifolds, Pure and Applied Mathematics, Vol. XV, Academic Press, New York, 1964.
  • [BM] R. Bott and J. Milnor, On the parallelizability of the spheres, Bull. Amer. Math. Soc. 64 (1958), 87–89.
  • [CG] J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. (2) 96 (1972), 413–443.
  • [E] D. Elerath, Open nonnegatively curved $3$-manifolds with a point of positive curvature, Proc. Amer. Math. Soc. 75 (1979), no. 1, 92–94.
  • [GW1] R. E. Greene and H. Wu, Curvature and complex analysis. II, Bull. Amer. Math. Soc. 78 (1972), 866–870.
  • [GW2] R. E. Greene and H. Wu, On the subharmonicity and plurisubharmonicity of geodesically convex functions, Indiana Univ. Math. J. 22 (1972/73), 641–653.
  • [GW3] R. E. Greene and H. Wu, Analysis on noncompact Kähler manifolds, Several complex variables (Proc. Sympos. Pure Math., Vol. XXX, Part 2, Williams Coll., Williamstown, Mass., 1975), Amer. Math. Soc., Providence, R.I., 1977, pp. 69–100.
  • [GW4] R. E. Greene and H. Wu, Function theory on manifolds which possess a pole, Lecture Notes in Mathematics, vol. 699, Springer, Berlin, 1979.
  • [GW5] R. E. Greene and H. Wu, On a new gap-phenomenon in Riemannian geometry, Amer. Math. Soc. 2 (June, 1981), 410, Abstracts.
  • [GW6] R. E. Greene and H. Wu, On a new gap phenomenon in Riemannian geometry, Proc. Nat. Acad. Sci. U.S.A. 79 (1982), no. 2, 714–715.
  • [GM] D. Gromoll and W. Meyer, On complete open manifolds of positive curvature, Ann. of Math. (2) 90 (1969), 75–90.
  • [HK] Th. Hasanis and D. Koutroufiotis, Flatness of Riemannian metrics outside compact sets, (preprint).
  • [K] M. Kervaire, Non-parallelizability of the $n$-sphere for $n>7$, Proc. Nat. Acad. Sci. 44 (1958), 280–283.
  • [KN] S. Kobayashi and K. Nomizu, Foundations of differential geometry. Vol. II, Interscience Tracts in Pure and Applied Mathematics, No. 15 Vol. II, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1969.
  • [MSY] N. Mok, Y.-T. Siu, and S.-T. Yau, The Poincaré-Lelong equation on complete Kähler manifolds, Compositio Math. 44 (1981), no. 1-3, 183–218.
  • [S] R. Sacksteder, On hypersurfaces with no negative sectional curvatures, Amer. J. Math. 82 (1960), 609–630.
  • [SY] Y.-T. Siu and S.-T. Yau, Complete Kähler manifolds with nonpositive curvature of faster than quadratic decay, Ann. of Math. (2) 105 (1977), no. 2, 225–264.
  • [W] F. W. Warner, Extensions of the Rauch comparison theorem to submanifolds, Trans. Amer. Math. Soc. 122 (1966), 341–356.