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arXiv · 2411.08748

Continuity of matings of Kleinian groups and polynomials

Miguel Ratis Laude
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Abstract

In recent years, the study of holomorphic correspondences as dynamical systems that can display behaviors of both rational maps and Kleinian groups has gained a good amount of attention. This phenomenon is related to the Sullivan dictionary, a list of parallels between the theories of these two systems. We build upon a surgical construction of such matings, due to Bullett and Harvey, increasing the degree of maps we consider, and proving regularity properties of the mating map on parameter spaces: namely, analyticity on the interior of its domain of definition, and continuity under quasiconformal rigidity on the boundary.

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Miguel Ratis Laude. 2025-07-01. Continuity of matings of Kleinian groups and polynomials. https://arxiv.org/abs/2411.08748

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