TL;DR
This paper introduces an infinite-dimensional generalization of the ADHM transform, extending its scope from finite-dimensional moduli spaces to boundary data and solutions of self-duality equations in a domain.
Contribution
It presents a novel infinite-parameter ADHM transform that maps boundary data to solutions of self-duality equations, broadening the transform's applicability.
Findings
Defines the infinite-parameter ADHM transform.
Establishes the transform as a map from boundary data to solutions.
Provides a framework for analyzing solutions in an infinite-dimensional setting.
Abstract
The Atiyah-Drinfeld-Hitchin-Manin (ADHM) transform and its various generalizations are examples of non-linear integral transforms between finite-dimensional moduli spaces. This note describes a natural infinite-dimansional generalization, where the transform becomes a map from boundary data to a family of solutions of the self-duality equations in a domain.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Waves and Solitons