Metrical and Dynamical Aspects in Complex Analysis by Léa Blanc-Centi

Author:Léa Blanc-Centi
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Remark 4.4.3

1.Proposition 4.4.2 was proven when Ω is bounded and ∂Ω is C ∞ in [31], when ∂Ω is C 1,1 and d = 2 in [50], and in full generality in [60].

2.By [28], if Ω is a convex set then ∂Ω contains a non-trivial complex affine disc if and only if ∂Ω contains a non-trivial holomorphic disc.

The proof of Proposition 4.4.2 is based on three ideas: 1.In a Gromov hyperbolic geodesic metric space, quasi-geodesics triangles are thin.

2.When is convex, straight lines can be parametrized as quasi-geodesics in (Ω, k Ω ).

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