Skip to main content
Log in

Closed geodesics on complete surfaces

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. Ballmann, W.: Der Satz von Lusternik und Schnirelmann. Bonn. Math. Schr.102, 1–25 (1978)

    Google Scholar 

  2. Bangert, V.: Konvexe Mengen in Riemannschen Mannigfaltigkeiten. Math. Z.162, 263–286 (1978)

    Google Scholar 

  3. Birkhoff, G.D.: Dynamical systems. Am. Math. Soc. Colloq. Publ., Vol. 9. Providence R.I.: Am. Math. Soc. 1927

    Google Scholar 

  4. Bleecker, D.D.: The Gauss-Bonnet inequality and almost-geodesic loops. Advances in Math.14, 183–193 (1974)

    Google Scholar 

  5. Cohn-Vossen, S.: Kürzeste Wege und Totalkrümmung auf Flächen. Compositio Math.2, 69–133 (1935)

    Google Scholar 

  6. Gromoll, D., Klingenberg, W., Meyer, W.: Riemannsche Geometrie im Großen. In: Lecture Notes in Mathematics, Vol. 55 Berlin, Heidelberg, New York: Springer 1968

    Google Scholar 

  7. Huber, A.: On subharmonic functions and differential geometry in the large. Comment. Math. Helv.32, 13–72 (1957)

    Google Scholar 

  8. Klingenberg, W.: Lectures on closed geodesics. Grundlehren der mathematischen Wissenschaften, Bd. 230. Berlin, Heidelberg, New York: Springer 1978

    Google Scholar 

  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. 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. 1966

  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. Morse, M.: The calculus of variations in the large. Am. Math. Soc. Colloq. Publ., Vol. 18. Providence, R.I.: Am. Math. Soc. 1934. Reprinted 1960

    Google Scholar 

  13. Poincaré, H.: Mécanique céleste. III. Paris: Gauthier-Villars 1899

    Google Scholar 

  14. Thom, R.: Stabilité structurelle et morphogénèse. Reading, Mass.: Benjamin 1972

    Google Scholar 

  15. Thorbergsson, G.: Closed geodesics on non-compact Riemannian manifolds. Math. Z.159, 249–258 (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Work partially supported by the program Sonderforschungsbereich “Theoretische Mathematik” at the University of Bonn

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bangert, V. Closed geodesics on complete surfaces. Math. Ann. 251, 83–96 (1980). https://doi.org/10.1007/BF01420283

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01420283

Keywords

Navigation