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arXiv · 2407.15976

Kobayashi hyperbolicity in Riemannian manifolds

Hervé Gaussier·Alexandre Sukhov
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Abstract

We study the boundary behavior of the Kobayashi-Royden metric and the Kobayashi hyperbolicity of domains in Riemannian manifolds. As an application, we prove a Fatou type theorem on the existence, almost everywhere, of non tangential limits for bounded conformal harmonic immersed discs. We also prove a Picard theorem for conformal harmonic discs and give some examples of Kobayashi hyperbolic Riemannian manifolds.

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Hervé Gaussier, Alexandre Sukhov. 2024-07-22. Kobayashi hyperbolicity in Riemannian manifolds. https://arxiv.org/abs/2407.15976

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