Geometric & Functional Analysis GAFA

, Volume 1, Issue 1, pp 14–79 | Cite as

Foliated plateau problem, part I: Minimal varieties

  • M. Gromov


Minimal Variety Plateau Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [And1]M. Anderson, Complete minimal varieties in hyperbolic space, Inv. Math. 69 (1982), 477–494.Google Scholar
  2. [And2]M. Anderson, Complete minimal hypersurfaces in hyperbolicn-manifolds, Comm. Math. Helv. 58 (1983), 254–290.Google Scholar
  3. [Ban1]V. Bangert, The existence of gaps in minimal foliations. (University of Waterloo) Aegu. Math. 34 (1987), 153–166.Google Scholar
  4. [Ban2]V. Bangert, A uniqueness theorem for ℤn-periodic variational problems, Comm. Math. Helv. 62 (1987), 511–531.Google Scholar
  5. [Ban3]V. Bagert, On minimal lamination of the torus, Ann. Inst. H. Poincaré 6:2 (1989), 95–138.Google Scholar
  6. [Ban4]V. Bangert, Lamination of 3-tori by least area surfaces, to appear in Moser anniversary volume.Google Scholar
  7. [Ban5]V. Bangert, Minimal geodesics, to appear in Erg. Th. and Dynam. Syst.Google Scholar
  8. [Bou-Ka]J.-P. Bourguignon andH. Karcher, Curvature operators: Pinching estimates and geometric examples, Ann. Scie. Ec. Norm. Sup. 4: 11 (1978), 71–92.Google Scholar
  9. [Ca-To]J.A. Carlson andD. Toledo, Harmonic mappings of Kähler manifolds to locally symmetric spaces, Publ. Math. 69 (1989), 173–201.Google Scholar
  10. [Che-Gr]J. Cheeger andM. Gromov, On characteristic numbers of complete manifolds of bounded curvature and finite volume, M.E. Rauch Mem. Vol. 1 (Charvel and Karkas, Eds.), Springer Berlin (1985), 115–154.Google Scholar
  11. [Conn]A. Connes, A survey of foliations and operator algebras, Proc. Symp. Pure Math. 38 (1982), Part I, 521–628.Google Scholar
  12. [Cor]K. Corlette, Archimedian superrigidity and hyperbolic geometry, Preprint, Univ. of Chicago, March 1990.Google Scholar
  13. [Gro1]M. Gromov, Filling Riemannian manifolds, Journ. Diff. Geom. 18 91983), 1–147.Google Scholar
  14. [Gro2]M. Gromov, Large Riemannian manifolds, in “Curv. and Top.” (Shoihama et al., eds), Lecture Notes in Math. 1201 (1986), 108–122.Google Scholar
  15. [Gro3]M. Gromov, Hyperbolic groups, in “Essays in Group Theory” (S.M. Gerten, Ed.) M.S.R.I. Publ. 8, Springer-Verlag (1987), 75–265.Google Scholar
  16. [Gro4]M. Gromov, Volume and bounded cohomology, Publ. Math. IHES 56 (1983), 213–307.Google Scholar
  17. [Gro7]M. Gromov, Hyperbolic manifolds, groups and actions, in “Riemannian surfaces and related topics”, Ann. Math. Studies 97 (1981), 183–215.Google Scholar
  18. [G-L1]M. Gromov andH.B. Lawson Jr., Spin and scalar curvature in the presence of a fundamental group, Ann. of Math. III (1980), 209–230.Google Scholar
  19. [G-L2]M. Gromov andH.B. Lawson Jr., Positive scalar curvature and Dirac operator on complete Riemannian manifolds, Publ. Math. IHES 58 (1983), 83–196.Google Scholar
  20. [G-L-P]M. Gromov, J. Lafontaine, andP. Pansu, Structures métriques pour les variétés riemanniennes, Cedic/Fernand Nathan, Paris 1981.Google Scholar
  21. [Her]L. Hernandez, Hermitian negative curvature operators, Preprint.Google Scholar
  22. [Hi-Pu]M. Hirsch andC. Pugh, Smoothness of horocycle foliation, Journ. Diff. Geom. 10 (1975), 225–238.Google Scholar
  23. [Law]H.B. Lawson Jr., Lectures on minimal submanifolds, Publish or Perish 1980.Google Scholar
  24. [Mat1]J. Mather, Minimal measures, Comm. Math. Helv. 64 (1989), 375–394.Google Scholar
  25. [Mat2]J. Mather, Action minimizing invariant measures for positive definite Lagrangian systems, preprint, Oct. 1989.Google Scholar
  26. [Mok]N. Mok, Metric rigidity theorems on Hermitian locally symmetric manifolds, World Scientific, Lec. in Pure Math. 3 (1989).Google Scholar
  27. [Mor]M. Morse, A fundamental class of geodesics on any closed surface of genus greater than one, Trans. Amer. Math. Soc. 26 (1924), 25–60.Google Scholar
  28. [Mos1]J. Moser, Minimal solutions of variational problems on a torus, Ann. Inst. M. Poincaré, An. non-lin. 3 (1986), 229–272.Google Scholar
  29. [Mos2]J. Moser, Minimal foliations on a torus, Preprint Sept. 1987.Google Scholar
  30. [Most]C.D. Mostow, Strong rigidity of locally symmetric spaces, Am. Math. Studies, Princeton, 78 (1973).Google Scholar
  31. [Pan1]P. Pansu, Une inégalité isopérimétrique sur le group d'Heisenberg, C.R. Acad. Sci. Paris 295 (1982), 127–131.Google Scholar
  32. [Pan2]P. Pansu, Metriques de Canot Caratheodory et quasi-isométries des espaces symétriques de rang un, Annals of Maths. 129:1 (1989), 1–61.Google Scholar
  33. [Sam]J.H. Sampson, Applications of harmonic maps to Kähler geometry, Contemp. Math. 49 (1986), 125–133.Google Scholar
  34. [Sch-Ya]R. Schoen andS.T. Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds of nonnegative scalar curvature, Ann. of Math. 110 (1979), 127–142.Google Scholar
  35. [Zim]R.J. Zimmer, Ergodic theory and semi-simple groups, Monogr. in Math., Birkäuser 1984.Google Scholar

Copyright information

© Birkhäuser Verlag 1991

Authors and Affiliations

  • M. Gromov
    • 1
  1. 1.IHESBures sur YvetteFrance

Personalised recommendations