Removable singularities and bubbling of harmonic maps and biharmonic maps

TL;DR

This paper proves theorems on removable singularities and bubbling phenomena for biharmonic and harmonic maps into non-positively curved manifolds, using Moser's iteration technique.

Contribution

It introduces new removable singularity theorems and bubbling results for biharmonic maps, extending understanding of their regularity and singularity behavior.

Findings

Removable singularity theorem for biharmonic maps' tension fields.

Bubbling theorem for biharmonic and harmonic maps.

Application of Moser's iteration technique to these problems.

Abstract

By using Moser's iteration technique, we show some removable singularity theorem of the tension field for biharmonic maps into manifolds of non-positive curvature, and the bubbling theorem of biharmonic maps and also harmonic maps.