Skip to main content
Log in

A uniqueness theorem for Zn-periodic variational problems

  • Published:
Commentarii Mathematici Helvetici

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. Aubry, S. andLe Daeron, P. Y.,The discrete Frenkel-Kontorova model and its extensions I—Exact results for the ground states, Physica8 D (1983), 381–422.

    Article  MathSciNet  Google Scholar 

  2. Bangert, V.,Mather sets for twist maps and geodesics on tori. To appear in Dynamics Reported, vol. 1.

  3. Freedman, M., Hass, J. andScott, P.,Least area incompressible surfaces in 3-manifolds, Invent. math.71 (1983), 609–642.

    Article  MATH  MathSciNet  Google Scholar 

  4. Giaquinta, M.,Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Ann. of Math. Studies105, Princeton N.J.: Princeton Univ. Press 1983.

    MATH  Google Scholar 

  5. Hedlund, G.A.,Geodesics on a two-dimensional Riemannian manifold with periodic coefficients, Ann. of Math.33 (1932), 719–739.

    Article  MathSciNet  Google Scholar 

  6. Ladyzhenskaya, O. A. andUral'tseva, N. N.,Linear and Quasilinear Elliptic Equations. New York-London: Academic Press 1968.

    MATH  Google Scholar 

  7. Mather, J. N.,Existence of quasi-periodic orbits for twist homeomorphisms of the annulus, Topology21 (1982), 457–467.

    Article  MATH  MathSciNet  Google Scholar 

  8. Morse, M.,A fundamental class of geodesics on any closed surface of genus greater than one, Trans. Am. Math. Soc.26 (1924), 25–60.

    Article  MathSciNet  Google Scholar 

  9. Moser, J.,Minimal solutions of variational problems on a torus, Ann. Inst. Henri Poincaré (Analyse non linéaire)3 (1986), 229–272.

    MATH  Google Scholar 

  10. Moser, J.,Recent developments in the theory of Hamiltonian systems. Preprint, Zürich 1985.

  11. Schoen, R. andYau, S. T.,Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature. Ann. of Math.110 (1979), 127–142.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bangert, V. A uniqueness theorem for Zn-periodic variational problems. Commentarii Mathematici Helvetici 62, 511–531 (1987). https://doi.org/10.1007/BF02564459

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02564459

Keywords

Navigation