Convergence of almost harmonic maps to geodesic bubble trees

TL;DR

This paper establishes a precise condition on the decay of tension in almost harmonic maps from degenerating surfaces, ensuring their convergence to a harmonic map-based limiting structure called a geodesic bubble tree.

Contribution

It provides a sharp criterion for the convergence of almost harmonic maps to geodesic bubble trees on degenerating surfaces.

Findings

Established a decay criterion for tension in almost harmonic maps.

Proved subconvergence to harmonic maps forming a geodesic bubble tree.

Enhanced understanding of harmonic map limits on degenerating surfaces.

Abstract

We prove a sharp criterion on the decay of the tension of almost harmonic maps from degenerating surfaces that ensures that such maps subconverge to a limiting object that is made up entirely of harmonic maps.