Local convexifiability of some rigid domains

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Authors	KOLÁŘ Martin
Year of publication	2005
Type	Article in Periodical
Magazine / Source	Supplemento ai Rendiconti del Circolo Matematico di Palermo,Serie II,
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	convexifiability; Kohn-Nirenberg phenomenon; finite type; rigid domains
Description	The main obstruction for constructing holomorphic reproducing kernels on weakly pseudoconvex domains is the Kohn-Nirenberg phenomenon, i.e., nonexistence of supporting functions and local nonconvexifiability. It is well known that domains of type four in C^2 do admit supporting functions at every boundary point, but still open is the question whether such domains are also locally convexifiable. This paper proves this under the additional assumption of rigidity of the domain.
Related projects:	Algebraic methods in geometric analysis and topology