References
Aubry, S.,The twist map, the extended Frenkel-Kontorova model and the devil's staircase. Physica7D (1983), 240–258.
Bangert, V.,Mather sets for twist maps and geodesics on tori. Dynamics Reported, Vol. 1 (in press).
Bangert, V.,A uniqueness theorem for ℤ n-periodic variational problems. Comment. Math. Helv.62 (1987) (in press).
Bokowski, J. andSperner, E.,Zerlegung konvexer Körper durch minimale Trennflächen. J. Reine Angew. Math.311/312 (1979), 80–100.
Courant, R.,Dirichlet's principle, conformal mapping and minimal surfaces. Interscience, New York, 1950.
Federer, H.,Geometric measure theory. (Grundlehren math. Wiss. Vol. 153). Springer, Berlin—Heidelberg—New York, 1969.
Hedlund, G. A.,Geodesics on a two-dimensional Riemannian manifold with periodic coefficients. Ann. of Math.33 (1932), 719–739.
John, F.,Partial Differential Equations, 3rd Ed. Springer, New York—Heidelberg—Berlin, 1980.
MacKay, R. S. andPercival, I. C.,Converse KAM: Theory and practice. Comm. Math. Phys.98 (1985), 301–311.
Mather, J. N. Non-existence of invariant circles. Erg. Th. Dynam. Sys.4 (1984), 301–309.
Mather, J. N.,A criterion for the non-existence of invariant circles. Inst. Hautes Études Sci. Publ. Math.63 (1986), 153–204.
Moser, J.,Monotone twist mappings and the calculus of variation. Ergodic Theory Dynamical Systems6 (1986), 325–333.
Moser, J.,Break-down of stability. In: Lect. Notes in Physics Vol. 247, J. M. Jowett, M. Month and S. Turner, Eds., Springer, Berlin—New York, 1986, pp. 492–518.
Moser, J. Recent developments in the theory of Hamiltonian systems. SIAM Review28 (1986), 459–485.
Moser, J. Minimal solutions of variational problems on torus, Ann. Inst. H. Poincaré (Analyse non linéaire)3 (1986), 229–272.
Simon, L. Lectures on geometric meaure theory. Proc. Centre Math. Analysis, Vol. 3. Australian National University, Canberra, 1983.
Solomon, B.,On foliations of ℝ n+1 by minimal hypersurfaces. Comment. Math. Helv.61 (1986), 67–83.
Author information
Authors and Affiliations
Additional information
Dedicated to Professor Otto Haupt with best wishes on his 100th birthday.
Rights and permissions
About this article
Cite this article
Bangert, V. The existence of gaps in minimal foliations. Aeq. Math. 34, 153–166 (1987). https://doi.org/10.1007/BF01830667
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01830667