Common Fixed Points in Hyperbolic Riemann Surfaces and Convex Domains

DOI10.2307/2048745zbMath0724.32012OpenAlexW4233047720MaRDI QIDQ5758455

Marco Abate, Vigué, Jean-Pierre

Publication date: 1991

Full work available at URL: https://doi.org/10.2307/2048745

zbMATH Keywords

Riemann surfaceiteration of holomorphic mapshyperbolic domainboundary of a convex domaincommuting family of self-mapsfixed points of self-maps

Mathematics Subject Classification ID

Invariant metrics and pseudodistances in several complex variables (32F45) Compact Riemann surfaces and uniformization (30F10) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (12)

Hyperbolic imbedding and spaces of continuous extensions of holomorphic maps ⋮ Theorems of Denjoy-Wolff type ⋮ Unnamed Item ⋮ Wolff-Denjoy theorems in nonsmooth convex domains ⋮ Results and conjectures in holomorphic fixed point theory ⋮ Fixed points and uniqueness of complex geodesics ⋮ Unnamed Item ⋮ Commuting holomorphic functions and hyperbolic automorphisms ⋮ Unnamed Item ⋮ Common fixed points of commuting holomorphic maps of the polydisc which are expanding on the torus ⋮ On holomorphic maps which commute with hyperbolic automorphisms ⋮ The existence and non-existence of common fixed points for commuting families of holomorphic mappings

Cites Work

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• Common fixed points of commuting holomorphic maps
• Holomorphic retracts in complex n-space
• Common fixed points of commuting holomorphic maps of the hyperball
• Vector fields on analytic spaces
• Hyperbolically imbedded spaces and the big Picard theorem
• Holomorphic idempotents and common fixed points on the 2-disk
• Commuting Analytic Functions
• Points Fixes D'Applications Holomorphes Dans Un Domaine Borne Convexe De C n
• On Fixed Points of Commuting Analytic Functions
• Commuting Functions with No Common Fixed Point
• On Common Fixed Points of Commuting Continuous Functions on an Interval

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