A Bounded Kohn Nirenberg Domain

Abstract

Abstract. Building on the famous domain of Kohn and Nirenberg we give an example of a domain which shares the important features of the Kohn Nirenberg domain, but which can also be shown to be φ-bounded.As an application, we remark that this example has compact automorphism group.

Proper holomorphic curves attached to domains

“…which is weakly pseudoconvex domain with smooth boundary that does not have a support hypersurface at 0. Calamai [5] constructed a bounded weakly pseudoconvex domain with smooth boundary that does not have a support hypersurface at 0. Kolář [17,18] constructed examples of smoothly bounded nonconvexifiable pseudoconvex domains with local support hypersurfaces.…”

“…10 + |wz| 2 < 0} has the following properties:• D is a bounded pseudoconvex domain in C 2 with smooth boundary, • D has a Stein Runge neighborhood basis, • 0 ∈ bD is a weakly pseudoconvex point of finite 1-type, • D is not locally convexifiable at 0, • D has a global support hypersurface at 0.The domain D is a modification of the Kohn-Nirenberg domainD ′ = {(z, w) ∈ C 2 : − ℜw + |z| 8 + 15 7 |z| 2 ℜ(z 6 ) + |wz| 2 < 0},which is weakly pseudoconvex domain with smooth boundary that does not have a support hypersurface at 0. Calamai[5] constructed a bounded weakly pseudoconvex domain with smooth boundary that does not have a support hypersurface at 0. Kolář [17, 18] constructed examples of smoothly bounded nonconvexifiable pseudoconvex domains with local support hypersurfaces.…”