@article{931bb069998f435c8db435dda979bcc4,
title = "On the complexity of proper holomorphic mappings between balls",
abstract = "This article contributes 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.",
keywords = "Balls, Complexity, Proper mappings",
author = "D'Angelo, {John P.} and Jiri Lebl",
note = "Funding Information: The first author acknowledges support from NSF grants DMS 05-00765 and DMS 07-53978. The authors began discussing this kind of problem at MSRI in 2005; the first author ran a graduate student experience in CR Geometry which the second author attended while a student. Both acknowledge support from MSRI. Both also acknowledge AIM for the meeting on Complexity Theory in CR Geometry held in 2007. Both authors also thank Han Peters, Xiaojun Huang, and Shanyu Ji for helpful discussions.",
year = "2009",
month = mar,
doi = "10.1080/17476930902759403",
language = "English (US)",
volume = "54",
pages = "187--204",
journal = "Complex Variables and Elliptic Equations",
issn = "1747-6933",
publisher = "Taylor and Francis Ltd.",
number = "3-4",
}