Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields: 0 (Frontiers in Mathematics)

Book Details

• Publisher: Birkhäuser

• Author: Yuan-Jen Chiang

• ISBN: 9783034805339

• Edition: 2013

• Binding: Paperback

• Pages: 399

• Release Date: 28-06-2013

• Languages: English

About The Book
"Harmonic Maps, Biharmonic Maps and Related Topics" by Yuan-Jen Chiang is a comprehensive study on the evolution and developments in the theory of harmonic and biharmonic maps, which play a significant role in both mathematics and physics. The book traces the historical roots of harmonic maps and their connection to Riemannian manifolds, starting with the seminal work of James Eells and Joseph H. Sampson in 1964. It also explores the progression from harmonic maps to more complex fields, such as wave maps, Yang-Mills fields, and the introduction of biharmonic maps by Guoying Jiang in 1986.

The author also introduces biwave maps, which generalize wave maps, and bi-Yang-Mills fields, which extend the concepts of Yang-Mills fields, topics first studied by Toshiyuki Ichiyama, Jun-Ichi Inoguchi, and Hajime Urakawa in 2008. Additionally, the book delves into exponential harmonic maps, exponential wave maps, and exponential Yang-Mills fields, presenting cutting-edge research and findings in these areas.

This book is an excellent resource for mathematicians and physicists interested in differential geometry, functional analysis, and the mathematical physics surrounding Yang-Mills theory and harmonic analysis. The work emphasizes the connections between different fields of study, offering a broad perspective on the ongoing advancements in these topics.

Key Features:

• In-depth exploration of harmonic maps, wave maps, Yang-Mills fields, and their generalizations.

• Historical context and important developments in the mathematical study of these fields.

• Introduction of biwave maps and bi-Yang-Mills fields, expanding existing theories.

• Emphasis on exponential maps and their relationship to the core subjects.

• A crucial resource for anyone working in differential geometry, mathematical physics, or functional analysis.

This book is perfect for graduate students, researchers, and professionals in fields like mathematics, physics, and engineering who are looking to explore the intricate relationships between these important mathematical concepts.