Skip to main content
SpringerLink
Log in

Splitting theorems for nonnegatively curved open manifolds with large ideal boundary

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • [BGS] Ballmann, W., Gromov, M., Schroeder, V.: Manifolds of Nonpositive Curvature. (Prog. Math., vol. 61) Boston Basel Stuttgart: Birkhäuser 1985

    MATH  Google Scholar 

  • [BJ] Bröcker, Th., Jänich, K.: Introduction to differential topology. New York: Cambridge University Press 1982

    MATH  Google Scholar 

  • [CG] Cheeger, J., Gromoll, D.: On the structure of complete manifolds of nonnegative curvature. Ann. Math.96, 413–443 (1972)

    Article  MathSciNet  Google Scholar 

  • [F] Fukaya, K.: Collapsing Riemannian manifolds to ones of lower dimensions. J. Differ. Geom.25, 139–156 (1987)

    MATH  MathSciNet  Google Scholar 

  • [GS1] Greene, R., Shiohama, K.: Convex function on complete noncompact manifolds: topological structure. Invent. Math.63, 129–157 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  • [GS2] Greene, R., Shiohama, K.: Convex functions on complete noncompact manifolds: differentiable structure. Ann. Sci. Éc. Norm. Supér., IV. Sér.14, 357–367 (1981)

    MATH  MathSciNet  Google Scholar 

  • [GW] Greene, R., Wu, H.: On the subharmonicity and plurisubharmonicity of geodesically convex functions. Indiana Univ. Math. J.22, 641–653 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  • [G] Gromov, M.: Structures métriques pour les variétés riemanniennes, redigé par J. Lafontaine et P. Pansu. (Textes Math. vol. 1) Paris: Edic/Fernand Nathan 1981

    MATH  Google Scholar 

  • [GS] Grove, K., Shiohama, K.: A generalized sphere theorem. Ann. Math.106, 201–211 (1977)

    Article  MathSciNet  Google Scholar 

  • [GP] Grove, K., Petersen, P.: Volume comparison à la Aleksandrov. (Preprint)

  • [K] Kasue, A.: A compactification of a manifold with asymptotically nonnegative curvature. Ann. Sci. Éc. Norm. Supér., IV. Sér.21, 593–622 (1988)

    MATH  MathSciNet  Google Scholar 

  • [O] Otsu, Y.: On manifolds of small excess. Am. J. Math. (to appear)

  • [Sr1] Sharafutdinov, V.A.: Complete open manifolds of nonnegative curvature. Sib. Math. Zh.15, 177–191 (1973)

    Google Scholar 

  • [Sr2] Sharafutdinov, V.A.: The Pogorelov-Klingenberg theorem for manifold homeomorphic toR n. Sib. Mat. Zh.18 (no. 4), 915–925 (1997)

    Google Scholar 

  • [Sr3] Sharafutdinov, V.A.: Convex sets in a manifold of nonnegative curvature. Mat. Zam.26 (no. 1), 129–136 (1979)

    MATH  MathSciNet  Google Scholar 

  • [S] Shiohama, K.: Topology of complete noncompact manifolds. In: Shiohama, K. (ed.) Geometry of Geodesics and Related Topics. (Adv. Stud. Pure Math., vol. 3, pp. 423–450) Tokyo: Kinokuniya 1984

    Google Scholar 

  • [SY] Shiohama, K., Yamaguchi, T.: Positively curved manifolds with restricted diameters. In: Shiohama, K. (ed.) Geometry of Manifolds. (Perspect. Math., vol. 8, pp. 345–350) Boston: Academic Press 1989

    Google Scholar 

  • [Sy1] Shioya, T.: The ideal boundaries of complete open surfaces. Tôhoku Math. J.43 (no. 1), 37–59 (1991)

    MATH  MathSciNet  Google Scholar 

  • [Sy2] Shioya, T.: The ideal boundaries of complete open surfaces admitting total curvaturec(M)=−∞. In: Shiohama, K. (ed.) Geometry of Manifolds. (Perspect. Math., vol. 8, pp. 351–364) Boston: Academic Press 1989

    Google Scholar 

  • [Sy3] Shioya, T.: The ideal boundaries and global geometric properties of complete open surfaces. Nagoya Math. J.120, 181–204 (1990)

    MATH  MathSciNet  Google Scholar 

  • [Sy4] Shioya, T.: Geometry of total curvature. Doctoral Thesis, Kyushu University (1990)

  • [W1] Walschap, G.: Nonnegatively curved manifolds with souls of codimension 2. J. Differ. Geom.27, 525–537 (1988)

    MATH  MathSciNet  Google Scholar 

  • [W2] Walschap, G.: A splitting theorem for 4-dimensional manifolds of nonnegative curvature. Proc. Am. Math. Soc.104, 265–268 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  • [Y] Yim, J.: Space of souls in a complete open manifold of nonnegative curvature. J. Differ. Geom.32, 429–455 (1990)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Kyushu University, 812, Fukuoka, Japan

    Takashi Shioya

Authors
  1. Takashi Shioya
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shioya, T. Splitting theorems for nonnegatively curved open manifolds with large ideal boundary. Math Z 212, 223–238 (1993). https://doi.org/10.1007/BF02571655

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02571655

Keywords

Search

Navigation