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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
—, “Necessary conditions for subellipticity of the \( \bar \partial \)-Neumann problem,” (preprint).
J. D’Angelo, “Sharp local bounds for orders of contact,” Proc. Nat. Acad. Sci. USA 78(1981), 3998–3999.
—, “Subelliptic estimates and failure of semi continuity for orders of contact,” Duke Math. J. 47(1980), 955–957.
—, “Real hypersurfaces, orders of contact, and applications,d” Annals of Math. (to appear).
P. Greiner, “On subelliptic estimates of the \( \bar \partial \)-Neumann problem,” J. Differential Geometry 9(1974), 239–250.
J. Kohn, “Boundary behavior of \( \bar \partial \) on weakly pseudoconvex manifolds of dimension two,” J. Differential Geometry 6(1972), 523–542.
—, “Subellipticity of the \( \bar \partial \)-Neumann problem on pseudoconvex domains: sufficient conditions,” Acta Math. 142(1979), 79–122.
L. Rothschild and E. Stein, “Hypoelliptic differential operators and nilpotent Lie groups,” Acta Math. 137(1976), 247–320.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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