Estimation of the Carathéodory distance on pseudoconvex domains of finite type whose boundary has Levi form of corank at most one
Annales Polonici Mathematici, Tome 109 (2013) no. 3, pp. 209-260
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
study class smooth bounded weakly pseudoconvex domains subset mathbb whose boundary points finite type sense kohn whose levi form has degenerate eigenvalue each boundary point prove effective estimates invariant distance carath odory completes authors investigations invariant differential metrics carath odory bergman kobayashi corank situation invariant distances pseudoconvex finite type domains dimension
Affiliations des auteurs :
Gregor Herbort 1
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author = {Gregor Herbort},
title = {Estimation of the {Carath\'eodory} distance on pseudoconvex domains of finite type whose boundary has {Levi} form of corank at most one},
journal = {Annales Polonici Mathematici},
pages = {209--260},
publisher = {mathdoc},
volume = {109},
number = {3},
year = {2013},
doi = {10.4064/ap109-3-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap109-3-1/}
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Gregor Herbort. Estimation of the Carathéodory distance on pseudoconvex domains of finite type whose boundary has Levi form of corank at most one. Annales Polonici Mathematici, Tome 109 (2013) no. 3, pp. 209-260. doi: 10.4064/ap109-3-1
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