Skip to main content

Local Bounds for Orders of Contact and a Conjecture about Subellipticity

  • Chapter
Several Complex Variables
  • 375 Accesses

Abstract

This work describes the local geometry of a real hypersurface of ℂn, and how it relates to subelliptic estimates for the \( \bar \partial \)-Neumann problem. The geometric results appear in (3,5); the results on subellipticity appear in the works of Kohn (7,8) and Catlin (1,2). In this paper we formulate a conjecture about the interplay between these subjects.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. D. Catlin, “Necessary conditions for subellipticity and hypoellipticity of the \( \bar \partial \)-Neumann problem on pseudoconvex domains,” Recent Developments in Several Complex Variables, Princeton Univ. Press, 1981.

    Google Scholar 

  2. —, “Necessary conditions for subellipticity of the \( \bar \partial \)-Neumann problem,” (preprint).

    Google Scholar 

  3. J. D’Angelo, “Sharp local bounds for orders of contact,” Proc. Nat. Acad. Sci. USA 78(1981), 3998–3999.

    Article  MathSciNet  MATH  Google Scholar 

  4. —, “Subelliptic estimates and failure of semi continuity for orders of contact,” Duke Math. J. 47(1980), 955–957.

    Article  MathSciNet  MATH  Google Scholar 

  5. —, “Real hypersurfaces, orders of contact, and applications,d” Annals of Math. (to appear).

    Google Scholar 

  6. P. Greiner, “On subelliptic estimates of the \( \bar \partial \)-Neumann problem,” J. Differential Geometry 9(1974), 239–250.

    MathSciNet  MATH  Google Scholar 

  7. J. Kohn, “Boundary behavior of \( \bar \partial \) on weakly pseudoconvex manifolds of dimension two,” J. Differential Geometry 6(1972), 523–542.

    MathSciNet  MATH  Google Scholar 

  8. —, “Subellipticity of the \( \bar \partial \)-Neumann problem on pseudoconvex domains: sufficient conditions,” Acta Math. 142(1979), 79–122.

    Article  MathSciNet  MATH  Google Scholar 

  9. L. Rothschild and E. Stein, “Hypoelliptic differential operators and nilpotent Lie groups,” Acta Math. 137(1976), 247–320.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Birkhäuser Boston, Inc.

About this chapter

Cite this chapter

D’Angelo, J.P. (1984). Local Bounds for Orders of Contact and a Conjecture about Subellipticity. In: Kohn, J.J., Remmert, R., Lu, QK., Siu, YT. (eds) Several Complex Variables. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-5296-2_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-5296-2_3

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3189-5

  • Online ISBN: 978-1-4612-5296-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics