Complex Variables Functions.–The stars at infinity in several complex variables

This text reviews certain notions in metric geometry that may have further applications to problems in complex geometry and holomorphic dynamics in several variables. The discussion contains a few new results and formulates a number of questions related to the asymptotic geometry and boundary estima...

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Vydáno v:Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni Ročník 35; číslo 1; s. 49
Hlavní autor: Karlsson, Anders
Médium: Journal Article
Jazyk:angličtina
Vydáno: European Mathematical Society Publishing House 01.01.2024
Témata:
Denjoy-Wolff theorems
Kahler geometry
Kobayashi pseudo-metric
random iterations
Teichmuller spaces
United States
ISSN:1120-6330, 1720-0768
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Shrnutí:This text reviews certain notions in metric geometry that may have further applications to problems in complex geometry and holomorphic dynamics in several variables. The discussion contains a few new results and formulates a number of questions related to the asymptotic geometry and boundary estimates of bounded complex domains, boundary extensions of biholomorphisms, the dynamics of holomorphic self-maps, Teichmuller theory, and the existence of constant scalar curvature metrics on compact Kahler manifolds. KEYWORDS.--Kobayashi pseudo-metric, Denjoy-Wolff theorems, Teichmuller spaces, Kahler geometry, random iterations, metric geometry. MATHEMATICS SUBJECT CLASSIFICATION 2020. - 32H50 (primary); 32Q45, 51F99, 32Q15, 32Hxx (secondary).
ISSN:1120-6330
1720-0768
DOI:10.4171/RLM/1033