Skip to main content

The trapping property of totally gedodesic hyperplanes in hadamard spaces

This is a preview of subscription content, access via your institution.

References

  1. V. Bangert, Laminations of 3-tori by least area surfaces, in “Analysis et cetera” (P.H. Rabinowitz, E. Zehnder, eds.), Academic Press, Boston, 1990, 85–114.

    Google Scholar 

  2. V. Bangert, U. Lang, Trapping quasiminimizing submanifolds in spaces of negative curvature, Comment. Math. Helv. 71 (1996), 122–143.

    Google Scholar 

  3. H. Federer, Geometric Measure Theory, Springer Verlag, Berlin, 1969.

    Google Scholar 

  4. H. Federer, The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension, Bull. Amer. Math. Soc. 76 (1970), 767–771.

    Google Scholar 

  5. M. Gromov, Hyperbolic groups, in “Essays in Group Theory” (S.M. Gersten, ed.), MSRI Publ. 8, Springer (1987), 75–263.

  6. M. Gromov, Foliated plateau problem, Part 1: Minimal varieties, GAFA 1 (1991), 14–79.

    Google Scholar 

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

    Google Scholar 

  8. W. Klingenberg, Geodätischer Fluss auf Mannigfaltigkeiten vom hyperbolischen Typ, Invent. Math. 14 (1971), 63–82.

    Google Scholar 

  9. U. Lang, Quasi-minimizing surfaces in hyperbolic space, Math. Z. 210 (1992), 581–592.

    Google Scholar 

  10. U. Lang, The existence of complete minimizing hypersurfaces in hyperbolic manifolds, Int. J. Math. 6 (1995), 45–58.

    Google Scholar 

  11. F. Morgan, Geometric Measure Theory. A Beginner's Guide, Academic Press, Boston, 1988.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  14. J. Moser, A stability theorem for minimal foliations on a torus, Ergod. Th. & Dynam. Sys. 8 (1988), 251–281.

    Google Scholar 

  15. L. Simon, Lectures on Geometric Measure Theory, Proc. Cent. Math. Anal. 3, Austr. Nat. U. Canberra, 1983.

  16. L. Simon, A strict maximum principle for area minimizing hypersurfaces, J. Diff. Geom. 26 (1987), 327–335.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lang, U. The trapping property of totally gedodesic hyperplanes in hadamard spaces. Geometric and Functional Analysis 6, 689–702 (1996). https://doi.org/10.1007/BF02247117

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02247117

Keywords