The right invariant metric on the analytic automorphism group of the unit open disk induced by maximal modulus
The right invariant metric on the analytic automorphism group of the unit open disk induced by maximal modulus
In this paper, we study the right invariant metric dH∞ on the analytic automorphism group Aut(D) of the unit open disk D induced by maximal modulus, that is, dH∞(φ,ψ) = sup|φ(z) − ψ(z)| for any φ,ψ ∈ Aut(D). We give the explicit formula of the right invariant metric dH∞ and characterize the almost regular Finsler geometric structure of (Aut(D), dH∞).
Complex Variables, Differential Geometry (math.DG), 53C60, 22F50, 54E35, Group Theory, Metric Geometry, FOS: Mathematics, Metric Geometry (math.MG), Group Theory (math.GR), Complex Variables (math.CV), Differential Geometry
Complex Variables, Differential Geometry (math.DG), 53C60, 22F50, 54E35, Group Theory, Metric Geometry, FOS: Mathematics, Metric Geometry (math.MG), Group Theory (math.GR), Complex Variables (math.CV), Differential Geometry
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