Estimation of the Carathéodory distance on pseudoconvex domains of finite type whose boundary has Levi form of corank at most one
Volume 109 / 2013
Annales Polonici Mathematici 109 (2013), 209-260
MSC: Primary 32F45; Secondary 32T25, 32T45.
DOI: 10.4064/ap109-3-1
Abstract
We study the class of smooth bounded weakly pseudoconvex domains $D\subset \mathbb C^n$ whose boundary points are of finite type (in the sense of J. Kohn) and whose Levi form has at most one degenerate eigenvalue at each boundary point, and prove effective estimates on the invariant distance of Carathéodory. This completes the author's investigations on invariant differential metrics of Carathéodory, Bergman, and Kobayashi in the corank one situation and on invariant distances on pseudoconvex finite type domains in dimension two.
