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Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, sometimes this metric satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity) and one can then use these conditions to understand the behavior of holomorphic maps.

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Gexin Yu

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