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\(\mathbb{D}^*\)-extension property without hyperbolicity. (English) Zbl 0927.37024
Summary: The authors present an example of a complex manifold \(X\) – in fact, a pseudoconvex open set in \(\mathbb{C}^2\) – such that \(X\) is not Kobayashi-hyperbolic, but any holomorphic map from the punctured unit disk to \(X\) extends to a map from the whole unit disk to \(X\).

MSC:
37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010)
37D05 Dynamical systems with hyperbolic orbits and sets
32D15 Continuation of analytic objects in several complex variables
32Q45 Hyperbolic and Kobayashi hyperbolic manifolds
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