• Corpus ID: 14246451

A new look at convexity and pseudoconvexity

@article{Krantz2007ANL,
  title={A new look at convexity and pseudoconvexity},
  author={Steven G. Krantz},
  journal={arXiv: Complex Variables},
  year={2007}
}
  • S. Krantz
  • Published 19 March 2007
  • Mathematics
  • arXiv: Complex Variables
We give a new characterization of pseudoconvex point, and of finite type point, using analytic discs. 
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References

SHOWING 1-10 OF 31 REFERENCES
Convex domains of finite type
Function theory in several complex variables
Fundamental theory: Holomorphic functions and domains of holomorphy Implicit functions and analytic sets The Poincare, Cousin, and Runge problems Pseudoconvex domains and pseudoconcave sets…
Several Complex Variables and the Geometry of Real Hypersurfaces
Holomorphic Functions and Mappings. Holomorphic Mappings and Local Algebra. Geometry of Real Hypersurfaces. Points of Finite Type. Proper Mappings between Balls. Geometry of the ?-Neumann Problem.…
A characterization of harmonic functions and points of finite and infinite type
Subelliptic Estimates for the ∂ -Neumann Problem for n - 1 Forms
In this note we deal with the problem of the subelliptic estimates of the 9-Neumann problem on nonpseudoconvex domains. In the first part we give a necessary condition for n 1 forms in a class of…
Domains with Non-Compact Automorphism Group: A Survey☆
Abstract We survey results arising from the study of domains in C n with non-compact automorphism group. Beginning with a well-known characterization of the unit ball, we develop ideas toward a…
Pseudoconvex domains: Bounded strictly plurisubharmonic exhaustion functions
The complex analysis of strictly pseudoconvex domains in IE" is rather well known, especially since the boundary regularity properties of solutions of the inhomogeneous Cauchy-Riemann equations…
Necessary Conditions for Subellipticity of the & 8706; -Neumann Problem
Let a be a a-closed form of type (p, q) with L2-coefficients on a smoothly bounded domain Q in C'. The problem of determining both the existence and regularity properties of the solution u of au = a,…
DIFFERENTIAL TOPOLOGY
This paper is to propose solutions to selected exercises in Differential Topology by Guillemin and Pollack, [1], and to comment on certain proofs in the book. Although the sections covered in this…
Real Submanifolds in Complex Space and Their Mappings
PrefaceCh. IHypersurfaces and Generic Submanifolds in C[superscript N]3Ch. IIAbstract and Embedded CR Structures35Ch. IIIVector Fields: Commutators, Orbits, and Homogeneity62Ch. IVCoordinates for…
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