Local asymptotics for Hitchin's equations and high energy harmonic maps
Nathaniel Sagman, Peter Smillie
TL;DR
This paper establishes new estimates and asymptotic decoupling phenomena for solutions to Hitchin's equations at high energy, extending previous results to all Higgs bundles and applying to harmonic maps and the Hitchin WKB problem.
Contribution
It introduces novel estimates and decoupling phenomena for Hitchin's equations applicable to all Higgs bundles, broadening the scope of previous regular semisimple results.
Findings
New estimates for high energy solutions
Asymptotic decoupling phenomenon identified
Applications to harmonic maps and Hitchin WKB problem
Abstract
We find new estimates and a new asymptotic decoupling phenomenon for solutions to Hitchin's self-duality equations at high energy. These generalize previous results for generically regular semisimple Higgs bundles to arbitrary Higgs bundles. We apply our estimates to the Hitchin WKB problem and to high energy harmonic maps to symmetric spaces and buildings.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Spectral Theory in Mathematical Physics · Differential Equations and Numerical Methods