This monograph presents recent and new ideas arising from the study of problems of planar fluid dynamics, and which are interesting from the point of view of geometric function theory and potential theory. the book is concerned with geometric problems for Hele-Shaw flows. Additionally, Hele-Shaw flows on parameter spaces are discussed, and connections with string theory are revealed. Assumes a graduate level understanding of real and complex analysis, and fluid mechanics.
Table of Contentsand Background.- Explicit Strong Solutions.- Weak Solutions and Balayage.- Geometric Properties.- Capacities and Isoperimetric Inequalities.- General Evolution Equations.- Hele-Shaw Evolution and Strings.