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Details
Title
Rational sphere maps / John P. D'Angelo.
Author
D'Angelo, John P.
ISBN
9783030758097 (electronic bk.)
3030758095 (electronic bk.)
3030758087
9783030758080
3030758095 (electronic bk.)
3030758087
9783030758080
Publication Details
Cham, Switzerland : Birkhäuser, 2021.
Language
English
Description
1 online resource
Item Number
10.1007/978-3-030-75809-7 doi
Call Number
QA406
Dewey Decimal Classification
515/.53
Summary
This monograph systematically explores the theory of rational maps between spheres in complex Euclidean spaces and its connections to other areas of mathematics. Synthesizing research from the last forty years, the author aims for accessibility by balancing abstract concepts with concrete examples. Numerous computations are worked out in detail, and more than 100 optional exercises are provided throughout for readers wishing to better understand challenging material. The text begins by presenting core concepts in complex analysis and a wide variety of results about rational sphere maps. The susbequent 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 problems will 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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed July 21, 2021).
Series
Progress in mathematics (Boston, Mass.) ; v. 341. 0743-1643
Available in Other Form
Print version: 9783030758080
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Table of Contents
Complex Euclidean Space
Examples and Properties of Rational Sphere Maps
Monomial Sphere Maps
Monomial Sphere Maps and Linear Programming
Groups Associated with Holomorphic Mappings
Elementary Complex and CR Geometry
Geometric Properties of Rational Sphere Maps
List of Open Problems.
Examples and Properties of Rational Sphere Maps
Monomial Sphere Maps
Monomial Sphere Maps and Linear Programming
Groups Associated with Holomorphic Mappings
Elementary Complex and CR Geometry
Geometric Properties of Rational Sphere Maps
List of Open Problems.