Nahm's equations and free-boundary problems

TL;DR

This paper explores the connections between free-boundary problems and infinite dimensional Lie groups, focusing on a version of Nahm's equations related to Hamiltonian diffeomorphisms in two dimensions.

Contribution

It introduces a novel perspective linking Nahm's equations with free-boundary problems within the context of infinite dimensional Lie groups.

Findings

Establishes a relationship between Nahm's equations and free-boundary problems.

Provides a new framework for understanding Hamiltonian diffeomorphisms.

Suggests potential applications in mathematical physics and geometry.

Abstract

This paper is a discussion of relations between some free-boundary problems and infinite dimensional Lie groups; particularly a version of Nahm's equations for the group of Hamiltonian diffeomorphisms in two dimensions.