The Lempert function of the symmetrized polydisc in higher dimensions is not a distance

DOI10.1090/S0002-9939-07-08817-XzbMath1123.32007arXivmath/0601367OpenAlexW1980759743MaRDI QIDQ5291939

Peter Pflug, Włodzimierz Zwonek, Nikolai Nikolov

Publication date: 19 June 2007

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

Full work available at URL: https://arxiv.org/abs/math/0601367

zbMATH Keywords

Lempert functionsymmetrized polydiscKobayashi distance and metricCaratheodory distance and metric

Mathematics Subject Classification ID

Invariant metrics and pseudodistances in several complex variables (32F45)

Related Items (18)

Bergman metric on the symmetrized bidisk and its consequences ⋮ A Schwarz lemma for the symmetrized polydisc via estimates on another family of domains ⋮ Interpolating functions for a family of domains related to \({\mu}\)-synthesis ⋮ Finite Blaschke products and the construction of rational \(\Gamma\)-inner functions ⋮ Balanced domains and convexity ⋮ Green functions of the spectral ball and symmetrized polydisk ⋮ The Friedrichs operator and circular domains ⋮ The complex geometry of a domain related to \(\mu\)-synthesis ⋮ 3-extremal holomorphic maps and the symmetrized bidisc ⋮ Function theoretic properties of symmetric powers of complex manifolds ⋮ Estimates of the Carathéodory metric on the symmetrized polydisc ⋮ Discontinuity of the Lempert function of the spectral ball ⋮ Automorphisms and the fundamental operators associated with the symmetrized tridisc ⋮ Algebraic properties of Toeplitz operators on the symmetrized polydisk ⋮ A Schwarz lemma for two families of domains and complex geometry ⋮ Characterizations of the symmetrized polydisc via another family of domains ⋮ Some Analysable Instances of μ-synthesis ⋮ Geometric properties of domains related to \(\mu\)-synthesis

Cites Work

• On infinitesimal behavior of the Kobayashi distance
• On the convexity of the Kobayashi metric on a taut complex manifold
• Geometry of the symmetrized polydisc
• The hyperbolic geometry of the symmetrized bidisc
• The symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domains
• ON THE DEFINITION OF THE KOBAYASHI–BUSEMAN PSEUDOMETRIC
• La métrique de Kobayashi et la représentation des domaines sur la boule
• THE SYMMETRIZED BIDISC AND LEMPERT'S THEOREM
• On the spectral Nevanlinna–Pick problem
• A note on Costara's paper
• Invariant distances and metrics in complex analysis–-revisited

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