Skip to main content
SpringerLink
Log in

On foliations of ℝn+1 by minimal hypersurfaces

  • Published:
Commentarii Mathematici Helvetici

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. F. Almgren,Some Interior Regularity Theorems for Minimal Surfaces and an Extension of Bernstein’s Theorem, Ann. of Math.84 (1966), 277–292.

    Article  MathSciNet  Google Scholar 

  2. E. Bombieri, E. DeGiorgi, andE. Giusti,Minimal Cones and the Bernstein Problem, Invent. Math.7 (1969), 243–268.

    Article  MATH  MathSciNet  Google Scholar 

  3. E. Bombieri andE. Giusti,Harnack’s Inequality for Elliptic Differential Equations on Minimal Surfaces, Invent. Math.15 (1972), 24–46.

    Article  MATH  MathSciNet  Google Scholar 

  4. L. Bers, F. John andM. Schecter,Partial Differential Equations, Lectures in Applied Mathematics, Vol. 3A, American Mathematical Society.

  5. E. DeGiorgi, Una Estension del Theorema di Bernstein, Ann. Scuola Norm. Pisa19 (1965), 79–85.

    MathSciNet  Google Scholar 

  6. H. Federer,Geometric Measure Theory, Springer-Verlag, New York, 1969.

    MATH  Google Scholar 

  7. D. Ferus andH. Karcher,Non-Rotational Minimal Spheres and Minimizing Cones, Comment. Math. Helv.60 (1985) No. 2 247–269.

    Article  MATH  MathSciNet  Google Scholar 

  8. W. H. Fleming,On the Oriented Plateau Problem, Rend. Circ. Mat. Palermo (2),11 (1962), 69–90.

    Article  MATH  MathSciNet  Google Scholar 

  9. P. Griffiths andJ. Morgan,Rational Homotopy Theory and Differential Forms, J. Coates, ed., Birkhauser, Boston, 1981.

    Google Scholar 

  10. D. Gilbarg andN. Trudinger,Elliptic Partial Differential Equations of Second Order, Springer-Verlag, New York, 1977.

    MATH  Google Scholar 

  11. A. Haefliger,Sur les Feuillitages des Variétés de Dimension n par des Feuilles Fermées de Dimension n − 1,Colloque de Topologie de Strasbourg, 1954–55, Institut de Mathematique, Université de Strasbourg.

  12. R. Harvey andH. B. Lawson,Calibrated Geometries, Acta Math.148 (1982), 47–157.

    Article  MATH  MathSciNet  Google Scholar 

  13. D. Hilbert andS. Cohn-Vossen,Geometry and the Imagination, Chelsea Publishing Company, New York, 1952.

    MATH  Google Scholar 

  14. A. Haefliger andG. Reeb,Varieties (Non Separees) a Une Dimension, et Structures Feuilletees du Plan, Enseignement Math. (2),3 (1957), 107–125.

    MATH  MathSciNet  Google Scholar 

  15. R. Hardt andL. Simon,Area-Minimizing Hypersurfaces with Isolated Singularities, Preprint (to appear in Crelle’s Journal).

  16. W.-Y. Hsiang andI. Sterling,On the Construction of Nonequatorial Minimal Hyperspheres in S n (1)with Stable Cones in ℝn+1. Proc. Nat. Acad. Sci. U.S.A.81 (1984) no. 24, Phys. Sci., 8035–8036.

    Article  MATH  MathSciNet  Google Scholar 

  17. W.-Y. Hsiang,Minimal Cones and the Spherical Bernstein Problem II, Invent. Math.74 (1983), 351–369.

    Article  MATH  MathSciNet  Google Scholar 

  18. M. Kervaire,Smooth Homology Spheres and Their Fundamental Groups, Trans. Amer. Math. Soc.144 (1969), 67–72.

    Article  MATH  MathSciNet  Google Scholar 

  19. J. Milnor,Lectures on the h-Cobordism Theorem, Princeton Mathematical Notes, Princeton University Press, Princeton, NJ, 1965.

    MATH  Google Scholar 

  20. D. Sullivan,A Homological Characterization of Foliations Consisting of Minimal Surfaces, Comment. Math. Helv.54 (1979), 218–223.

    Article  MATH  MathSciNet  Google Scholar 

  21. L. Simon,Lectures on Geometric Measure Theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, Canberra, Vol. 3, 1983.

    Google Scholar 

  22. P. Tomter,The Spherical Bernstein Problem in Even Dimensions, Preprint, Oslo Math. Inst. (1983).

  23. S. T. Yau, Problem Section, Seminar on Differential Geometry,Ann. of Math. Studies, No.192, Princeton University Press, Princeton, NJ (1982), 664–706.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Indiana University, 47405, Bloomington, IN

    Bruce Solomon

Authors
  1. Bruce Solomon
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Solomon, B. On foliations of ℝn+1 by minimal hypersurfaces. Commentarii Mathematici Helvetici 61, 67–83 (1986). https://doi.org/10.1007/BF02621903

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02621903

Keywords

Search

Navigation