Overview
- Synthesizes research from the past 40 years on rational sphere maps
- Explores connections with other areas of mathematics, such as combinatorics, optimization, and number theory
- Includes several computational examples worked out in detail
Part of the book series: Progress in Mathematics (PM, volume 341)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (8 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
The text begins by presenting core concepts in complex analysis and a wide variety of results about rational sphere maps. The subsequent chapters discuss combinatorial and optimization results about monomial sphere maps, groups associated with rational sphere maps, relevant complex and CR geometry, and some geometric properties of rational sphere maps. Fifteen open problems appear in the final chapter, with references provided to appropriate parts of the text. These problemswill encourage readers to apply the material to future research.
Rational Sphere Maps will be of interest to researchers and graduate students studying several complex variables and CR geometry. Mathematicians from other areas, such as number theory, optimization, and combinatorics, will also find the material appealing.
See the author’s research web page for a list of typos, clarifications, etc.: https://faculty.math.illinois.edu/~jpda/research.html
Reviews
“This monographs endeavors to provide analogous interesting features relevant to this subject. In particular, it explores the recent developments in the theory of rational sphere maps between complex spheres. It also establishes well the interrelation of this theory in several other relevant fields and its wide area of application. This monograph pays notable attention to computational aspects of the theory. The examples provided in each chapter explain well the theory from this constructive point of view." (Masoud Sabzevari, zbMATH 1485.32001, 2022)
“Many exercises are interspersed throughout the book to keep the reader interested and give a nice break to simply reading through. They are well worth thinking about. The book should be a good fit for a beginning graduate student who has finished their comprehensive or qualifying exams and is looking for a problem to study. … It is also a good read for an expert in a related field searching for new problems to study.” (Jiří Lebl, Mathematical Reviews, May, 2022)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Rational Sphere Maps
Authors: John P. D’Angelo
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-030-75809-7
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-75808-0Published: 12 July 2021
Softcover ISBN: 978-3-030-75811-0Published: 13 July 2022
eBook ISBN: 978-3-030-75809-7Published: 12 July 2021
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XIII, 233
Number of Illustrations: 1 b/w illustrations, 1 illustrations in colour
Topics: Several Complex Variables and Analytic Spaces, Global Analysis and Analysis on Manifolds, Differential Geometry