On the complexity of proper holomorphic mappings between balls
John P D'Angelo, Jiri Lebl
TL;DR
This paper advances the understanding of proper holomorphic mappings between balls by providing degree estimates, revealing a new gap phenomenon, and exploring inverse image properties.
Contribution
It introduces a degree estimate for rational proper maps, uncovers a new gap phenomenon for convex families, and studies inverse images in proper holomorphic mappings.
Findings
Degree estimate for rational proper maps
Discovery of a new gap phenomenon
Results on inverse images in proper maps
Abstract
We make several new contributions to the study of proper holomorphic mappings between balls. Our results include a degree estimate for rational proper maps, a new gap phenomenon for convex families of arbitrary proper maps, and an interesting result about inverse images.
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