Exponential transforms, resultants and moments
Bj\"orn Gustafsson
TL;DR
This paper reviews recent advances in harmonic moments, exponential transforms, and resultants of plane domains, highlighting their connections to mathematical physics, domain deformations, and integrable systems.
Contribution
It synthesizes recent developments linking harmonic moments, exponential transforms, and resultants with applications in mathematical physics and integrable structures.
Findings
Connections between harmonic moments and exponential transforms
Relationship of resultants to domain deformations
Applications to Laplacian growth and integrable systems
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.
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Taxonomy
TopicsNumerical methods in inverse problems · Advanced Mathematical Modeling in Engineering · Geometric Analysis and Curvature Flows