On local convexifiability of type four domains in $\bold C^2$

Martin Kol

E-mail: mkolar@math.muni.cz

Abstract. Results of Kohn-Nirenberg and Fornaess lead to the conjecture that any pseudoconvex domain in $\Bbb C^2$ with real analytic boundary is convexifiable in a neighbourhood of a point of finite type four. We prove this under an additional assumption on the model domain at the point. Techniques from the construction of Moser normal form are used as a main tool.

AMSclassification. 32F15

Keywords. Finite type, weakly pseudoconvex domains, Kohn-Nirenberg example, convexity and convexifiability, type four