Complex Geodesics and Iterates of Holomorphic Maps on Convex Domains in C n

DOI10.2307/2154452zbMath0790.32026OpenAlexW4230861162MaRDI QIDQ4201534

Peter R. Mercer

Publication date: 25 August 1993

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2154452

zbMATH Keywords

iterationKobayashi distancebounded convex domainhorospherecomplex geodesic

Mathematics Subject Classification ID

Invariant metrics and pseudodistances in several complex variables (32F45) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Boundary regularity of mappings in several complex variables (32H40)

Related Items (22)

The Lindelöf principle and angular derivatives in convex domains of finite type ⋮ Subelliptic estimates from Gromov hyperbolicity ⋮ Visibility of Kobayashi geodesics in convex domains and related properties ⋮ Gromov hyperbolicity and the Kobayashi metric on convex domains of finite type ⋮ Comparison and localization of invariant functions on strongly pseudoconvex domains ⋮ Separation of boundary singularities for holomorphic generators ⋮ Unbounded visibility domains, the end compactification, and applications ⋮ On the continuous extension of Kobayashi isometries ⋮ Bi-Hölder extensions of quasi-isometries on pseudoconvex domains of finite type in \(\mathbb{C}^2\) ⋮ Gromov hyperbolicity, the Kobayashi metric, and $\mathbb {C}$-convex sets ⋮ The Denjoy-Wolff theorem in \(\mathbb C^n\) ⋮ Localization of the Kobayashi metric and applications ⋮ Estimates of invariant distances on ``convex domains ⋮ Characterizing domains by the limit set of their automorphism group ⋮ Goldilocks domains, a weak notion of visibility, and applications ⋮ Boundary behavior of the Kobayashi distance in pseudoconvex Reinhardt domains ⋮ Complex geodesics, their boundary regularity, and a Hardy-Littlewood-type lemma ⋮ A form of Schwarz's lemma and a bound for the Kobayashi metric on convex domains ⋮ Iterates of holomorphic self-maps on pseudoconvex domains of finite and infinite type in $\mathbb C^n$ ⋮ Asymptotic total geodesy of local holomorphic curves exiting a bounded symmetric domain and applications to a uniformization problem for algebraic subsets ⋮ Bi-Hölder extensions of quasi-isometries on complex domains ⋮ A metric analogue of Hartogs' theorem

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