Duke Mathematical Journal

Splitting of nonnegatively curved leaves in minimal sets of foliations

Scot Adams and Garrett Stuck

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Article information

Source
Duke Math. J. Volume 71, Number 1 (1993), 71-92.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077289837

Mathematical Reviews number (MathSciNet)
MR1230286

Zentralblatt MATH identifier
0793.53032

Digital Object Identifier
doi:10.1215/S0012-7094-93-07104-9

Subjects
Primary: 53C12: Foliations (differential geometric aspects) [See also 57R30, 57R32]
Secondary: 58F18

Citation

Adams, Scot; Stuck, Garrett. Splitting of nonnegatively curved leaves in minimal sets of foliations. Duke Mathematical Journal 71 (1993), no. 1, 71--92. doi:10.1215/S0012-7094-93-07104-9. http://projecteuclid.org/euclid.dmj/1077289837.


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References

  • [Ada1] S. Adams, Superharmonic functions on foliations, Trans. Amer. Math. Soc. 330 (1992), no. 2, 625–635.
  • [Ada2] S. Adams, Generalities on amenable actions, preprint.
  • [AF1] S. Adams and A. Freire, Nonnegatively curved leaves in foliations, J. Differential Geom. 34 (1991), no. 3, 681–700.
  • [Arv1] W. Arveson, An invitation to $C^*$-algebras, Grad. Texts in Math., vol. 39, Springer-Verlag, New York, 1976.
  • [BC1] R. Bishop and R. Crittenden, Geometry of Manifolds, Pure Appl. Math., vol. 15, Academic Press, New York, 1964.
  • [BHC] A. Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485–535.
  • [BD1] T. Bröcker and T. tom Dieck, Representations of Compact Lie Groups, Grad. Texts in Math., vol. 98, Springer-Verlag, New York, 1985.
  • [Bo1] A. Borel, Density properties for certain subgroups of semisimple groups without compact components, Ann. of Math. (2) 72 (1960), 179–188.
  • [CG1] J. Cheeger and D. Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geom. 6 (1971), 119–128.
  • [CG2] J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. (2) 96 (1972), 413–443.
  • [Kec1] A. Kechris, Countable sections for locally compact group actions, preprint.
  • [Law1] H. B. Lawson, The Quantitative Theory of Foliations, CBMS Regional Conf. Ser. in Math., vol. 27, Amer. Math. Soc., Providence, 1977.
  • [Mag1] W. Magnus, Residually finite groups, Bull. Amer. Math. Soc. 75 (1969), 305–316.
  • [Ma1] G. Margulis, Quotient groups of discrete groups and measure theory, Funct. Anal. Appl. 12 (1978), 295–305.
  • [Mo1] P. Molino, Riemannian Foliations, Progr. Math., vol. 73, Birkhäuser, Boston, 1988.
  • [MZ1] D. Montgomery and L. Zippin, Topological Transformation Groups, Intersci. Tracts Pure Appl. Math., Wiley-Interscience, New York, 1955, 1965 reprinting has additional bibliography.
  • [Pla1] J. Plante, Foliations with measure preserving holonomy, Ann. of Math. (2) 102 (1975), no. 2, 327–361.
  • [Sc1] P. Scott, The geometries of $3$-manifolds, Bull. London Math. Soc. 15 (1983), no. 5, 401–487.
  • [SZ1] G. Stuck and R. J. Zimmer, Stabilizers for ergodic actions of higher rank semisimple groups, preprint.
  • [Var1] V. Varadarajan, Lie Groups, Lie Algebras and Their Representations, Grad. Texts in Math., vol. 102, Springer-Verlag, New York, 1984.
  • [Vee1] W. Veech, Topological dynamics, Bull. Amer. Math. Soc. 83 (1977), no. 5, 775–830.
  • [War1] F. Warner, Foundations of Differentiable Manifolds and Lie Groups, Grad. Texts in Math., vol. 94, Springer-Verlag, New York, 1983.
  • [Zim1] R. Zimmer, Ergodic theory, semisimple Lie groups and foliations by manifolds of negative curvature, Inst. Hautes Études Sci. Publ. Math. 55 (1982), 37–62.
  • [Zim2] R. Zimmer, Ergodic Theory and Semisimple Groups, Monographs in Mathematics, vol. 81, Birkhäuser, Boston, 1984.