Laplacian Growth on Branched Riemann Surfaces

Björn Gustafsson, Yu-Lin Lin

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English

Springer Nature Switzerland AG
23 March 2021

Calculus & mathematical analysis; Complex analysis, complex variables; Differential calculus & equations; Mathematical physics; Mechanics of fluids

Series: Lecture Notes in Mathematics

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.

By: Björn Gustafsson, Yu-Lin Lin
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 1st ed. 2021
Volume: 2287
Dimensions: Height: 235mm, Width: 155mm,
Weight: 454g
ISBN: 9783030698621
ISBN 10: 3030698629
Series: Lecture Notes in Mathematics
Pages: 156
Publication Date: 23 March 2021
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for Laplacian Growth on Branched Riemann Surfaces

“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)