Bounded domains on Kobayashi hyperbolic manifolds covering compact complex manifolds

2025/04/04 by Newsome, Nicholas
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.03935

Abstract

The lack of a uniformization theorem in several complex variables leads to a desire to classify all of the simply connected domains. We use established computational methods and a localization technique to generalize a recently-published classification. In particular, we show that if a domain with C^1,1 boundary on a Kobayashi hyperbolic complex manifold contains a totally real boundary point and covers a compact manifold, then its universal cover must be the Euclidean ball.

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