Rational Sphere Maps

John P. D'Angelo, PhD, is a Professor in the Department of Mathematics at the University of Illiniois at Urbana-Champaign, USA

“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)

• 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.