Overview
- Explores unsolved problems and new directions related to domain evolutions on Riemann surfaces
- Presents potentially fruitful ideas around the ill-posed suction problem
- Gives elementary, but intriguing, examples involving only polynomials and rational functions
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2287)
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About this book
This book studies solutions of the Polubarinova–Galin and Löwner–Kufarev equations, which describe the evolution of a viscous fluid (Hele-Shaw) blob, after the time when these solutions have lost their physical meaning due to loss of univalence of the mapping function involved. When the mapping function is no longer locally univalent interesting phase transitions take place, leading to structural changes in the data of the solution, for example new zeros and poles in the case of rational maps.
This topic intersects with several areas, including mathematical physics, potential theory and complex analysis. The text will be valuable to researchers and doctoral students interested in fluid dynamics, integrable systems, and conformal field theory.
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Reviews
“This interesting book is devoted to the Laplacian growth on Riemann surfaces. … This book is a valuable contribution to the modern theory of Laplacian growth. It contains many useful and interesting results, together with a rigorous analysis of all treated problems.” (Mirela Kohr, zbMATH 1526.30032, 2024)
Authors and Affiliations
Bibliographic Information
Book Title: Laplacian Growth on Branched Riemann Surfaces
Authors: Björn Gustafsson, Yu-Lin Lin
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-69863-8
Publisher: Springer 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
Softcover ISBN: 978-3-030-69862-1Published: 23 March 2021
eBook ISBN: 978-3-030-69863-8Published: 22 March 2021
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 156
Number of Illustrations: 1 b/w illustrations, 12 illustrations in colour
Topics: Functions of a Complex Variable, Analysis, Potential Theory, Mathematical Methods in Physics, Materials Science, general