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arXiv · 2606.10729

Uniformization of domains in the Riemann sphere via the Kobayashi metric

Jaikrishnan Janardhanan
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Abstract

We prove the uniformization theorem for domains in the Riemann sphere via the Kobayashi metric. Our proof does not rely on the existence of the elliptic modular function and instead uses the characterization of complete Kobayashi hyperbolicity for domains in the sphere.

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Jaikrishnan Janardhanan. 2026-06-09. Uniformization of domains in the Riemann sphere via the Kobayashi metric. https://arxiv.org/abs/2606.10729

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