$\mathbb{D}^\star$ extension property without hyperbolicity Do Duc ThaiPacal Thomas 32D1532H1532F4532D2032A07continuation of analytic objectsInvariant metrics and pseudodistancesremovable singularitiesHartogs domainsKobayashi hyperbolicity We 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 $X$. Indiana University Mathematics Journal 1998 text pdf 10.1512/iumj.1998.47.1484 10.1512/iumj.1998.47.1484 en Indiana Univ. Math. J. 47 (1998) 1125 - 1130 state-of-the-art mathematics http://iumj.org/access/