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.
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