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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