Mathematische Annalen

, Volume 251, Issue 1, pp 83–96 | Cite as

Closed geodesics on complete surfaces

  • Victor Bangert
Article

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References

  1. 1.
    Ballmann, W.: Der Satz von Lusternik und Schnirelmann. Bonn. Math. Schr.102, 1–25 (1978)Google Scholar
  2. 2.
    Bangert, V.: Konvexe Mengen in Riemannschen Mannigfaltigkeiten. Math. Z.162, 263–286 (1978)Google Scholar
  3. 3.
    Birkhoff, G.D.: Dynamical systems. Am. Math. Soc. Colloq. Publ., Vol. 9. Providence R.I.: Am. Math. Soc. 1927Google Scholar
  4. 4.
    Bleecker, D.D.: The Gauss-Bonnet inequality and almost-geodesic loops. Advances in Math.14, 183–193 (1974)Google Scholar
  5. 5.
    Cohn-Vossen, S.: Kürzeste Wege und Totalkrümmung auf Flächen. Compositio Math.2, 69–133 (1935)Google Scholar
  6. 6.
    Gromoll, D., Klingenberg, W., Meyer, W.: Riemannsche Geometrie im Großen. In: Lecture Notes in Mathematics, Vol. 55 Berlin, Heidelberg, New York: Springer 1968Google Scholar
  7. 7.
    Huber, A.: On subharmonic functions and differential geometry in the large. Comment. Math. Helv.32, 13–72 (1957)Google Scholar
  8. 8.
    Klingenberg, W.: Lectures on closed geodesics. Grundlehren der mathematischen Wissenschaften, Bd. 230. Berlin, Heidelberg, New York: Springer 1978Google Scholar
  9. 9.
    Klingenberg, W.: Closed geodesics on surfaces of genus 0. Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat.6, 19–38 (1979)Google Scholar
  10. 10.
    Lusternik, L.: The topology of the calculus of variations in the large. Trudy Mat. Inst. Steklov19, (1947) Translations of Mathematical Monographs, Vol. 16. Providence, R.I.: Am. Math. Soc. 1966Google Scholar
  11. 11.
    Lusternik, L., Schnirelmann, L.: Sur le problème de trois géodésiques fermées sur les surfaces de genre 0. C.R. Acad. Sci. Ser. A189, 269–271 (1929)Google Scholar
  12. 12.
    Morse, M.: The calculus of variations in the large. Am. Math. Soc. Colloq. Publ., Vol. 18. Providence, R.I.: Am. Math. Soc. 1934. Reprinted 1960Google Scholar
  13. 13.
    Poincaré, H.: Mécanique céleste. III. Paris: Gauthier-Villars 1899Google Scholar
  14. 14.
    Thom, R.: Stabilité structurelle et morphogénèse. Reading, Mass.: Benjamin 1972Google Scholar
  15. 15.
    Thorbergsson, G.: Closed geodesics on non-compact Riemannian manifolds. Math. Z.159, 249–258 (1978)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Victor Bangert
    • 1
  1. 1.Mathematisches Institut der UniversitätFreiburgFederal Republic of Germany

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