Finite type domains with hyperbolic orbit accumulation points

2013/04/30 by Bingyuan Liu, Liu, Bingyuan
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.1305.0046

rewrite the section 3, a new figure

arxiv created 2014/01/13 · arxiv updated 2014/01/14

Abstract

In this paper, finite type domains with hyperbolic orbit accumulation points are studied. We prove, in case of ℂ², it has to be a (global) pseudoconvex domain, after an assumption of boundary regularity. Moreover, one of the applications will realize the classification of domains within this class, precisely the domain is biholomorphic to one of the ellipsoids \lbrace (z, w): | z|^2m+| w|²<1, m∈ℤ⁺\rbrace. This application generalizes \citeBP98 in which the boundary is assumed to be real analytic for the case of hyperbolic orbit accumulation points.

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