Skip to main content

L2harmonic forms on complete Riemannian manifolds

  • Conference paper
  • First Online:
Geometry and Analysis on Manifolds

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1339))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. T. Anderson, L2harmonic forms and a conjecture of Dodziuk-Singer, Bulletin Amer. Math. Soc. 13 (1985), 163–165.

    Article  MATH  Google Scholar 

  2. M. F. Atiyah, Elliptic operators, discrete groups and Von Neumann algebras, Asterisque, 32–33 (1976), 43–72.

    MathSciNet  MATH  Google Scholar 

  3. R. Bishop and B. O'Neill, Manifolds of negative curvature. Trans. Amer. Math. Soc. 145 (1969), 1–49.

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Borel and N. Wallach, Continuous cohomology, discrete subgroups and representations of reductive groups, Ann. of Math. Studies, vol. 104 (1980).

    Google Scholar 

  5. R. Brooks, The fundamental group and spectrum of the Laplacian, Comm. Math. Helv. 36 (1981), 581–598.

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Cheeger, M. Goresky and R. Macpherson, L2cohomology and intersection homology of singular algebraic varieties, Ann. of Math. Studies, vol. 102 (1982), 303.

    MathSciNet  MATH  Google Scholar 

  7. J. Cheeger and M. Gromov, On the characteristic numbers of complete manifolds of bounded curvature and finite volume, Rauch Memorial Volume, I. Chavel and H. Farkas, Eds., Springer Verlag, Berlin (1985), 115–154.

    Google Scholar 

  8. J. Cheeger and M. Gromov, Bounds on the Von Neumann dimension of L2cohomology and the Gauss-Bonnet Theorem for open manifolds, Jour. Diff. Geo. 21 (1985), 1–34.

    MathSciNet  MATH  Google Scholar 

  9. J. Cheeger and M. Gromov, L2cohomology and group cohomology, Topology 25 (1986), 189–215.

    Article  MathSciNet  MATH  Google Scholar 

  10. G. deRham, Varietes differentiables, Hermann, Paris (1960).

    Google Scholar 

  11. J. Dodziuk, DeRham-Hodge theory for L2cohomology of infinite coverings, Topology, 16 (1977), 157–165.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Dodziuk, Sobolev spaces of differential forms and deRham-Hodge isomorphism, J. Diff. Geo. 16 (1981), 63–73.

    MathSciNet  MATH  Google Scholar 

  13. J. Dodziuk, L2harmonic forms on complete manifolds, Ann. of Math. Studies, vol. 102 (1982), 191–302.

    Google Scholar 

  14. H. Donnelly and F. Xavier, On the differential form spectrum of negatively curved Riemannian manifolds, Amer. J. Math 108 (1984), 169–185.

    Article  MathSciNet  MATH  Google Scholar 

  15. H. Donnelly and C. Fefferman, L2cohomology and index theorem for the Bergmann metric, Ann. of Math. 118 (1983), 593–618.

    Article  MathSciNet  MATH  Google Scholar 

  16. M. Gaffney, The heat equation method of Milgram and Rosenblum for open Riemannian manifolds, Ann. of Math. 60 (1954), 458–466.

    Article  MathSciNet  MATH  Google Scholar 

  17. S. Gallot and D. Meyer, Operateur de courbure et Laplacien des formes differentielles d'une variete riemannienne, J. Math. Pure Appl. 54 (1975), 259–284.

    MathSciNet  MATH  Google Scholar 

  18. D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order, Springer Verlag, New York (1977).

    Book  MATH  Google Scholar 

  19. D. Gromoll and W. Meyer, On complete open manifolds of positive curvature, Ann. of Math. 90 (1979), 74–90.

    MathSciNet  MATH  Google Scholar 

  20. K. Kodaira, Harmonic fields in Riemannian manifolds, Ann. of Math. 50 (1949), 587–665.

    Article  MathSciNet  MATH  Google Scholar 

  21. T. Lyons and D. Sullivan, Function theory, random paths and covering spaces, Jour. Diff. Geo., 19 (1984), 299–323.

    MathSciNet  MATH  Google Scholar 

  22. R. Mazzeo, MIT Thesis (1986).

    Google Scholar 

  23. H. Sealey, Some conditions ensuring the vanishing of harmonic differential forms..., Math. Proc. Camb. Phil. Soc. 91 (1982), 441–452.

    Article  MathSciNet  MATH  Google Scholar 

  24. S. Zucker, L2cohomology of warped products and arithmetic groups, Inv. Math. 70 (1982), 169–218.

    Article  MathSciNet  MATH  Google Scholar 

  25. S.-T. Yau, Problem section, Seminar on Differential Geometry, Ann. of Math. Studies vol. 102 (1982).

    Google Scholar 

Download references

Authors

Editor information

Toshikazu Sunada

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Anderson, M.T. (1988). L2harmonic forms on complete Riemannian manifolds. In: Sunada, T. (eds) Geometry and Analysis on Manifolds. Lecture Notes in Mathematics, vol 1339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083043

Download citation

  • DOI: https://doi.org/10.1007/BFb0083043

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50113-8

  • Online ISBN: 978-3-540-45930-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics