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Exponential Transforms, Resultants and Moments

  • Björn GustafssonEmail author
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

We give an overview of some recent developments concerning harmonic and other moments of plane domains, their relationship to the Cauchy and exponential transforms, and to the meromorphic resultant and elimination function. The paper also connects to certain topics in mathematical physics, for example domain deformations generated by harmonic gradients (Laplacian growth) and related integrable structures.

Keywords

Cauchy transform Elimination function Exponential transform Laplacian growth Moment Polubarinova–Galin equation Quadrature domain Resultant String equation 

Notes

Acknowledgments

This work has been performed within the framework of the European Science Foundation Research Networking Programme HCAA and has been supported by the Swedish Research Council and the Göran Gustafsson Foundation.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsKTHStockholmSweden

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