The profile of bubbling solutions of a class of fourth order geometric equations on 4-manifolds

TL;DR

This paper investigates the behavior of solutions to a class of fourth order geometric equations on 4-manifolds, providing precise estimates on how solutions resemble standard bubbles near blow-up points.

Contribution

It offers sharp estimates on the difference between bubbling solutions and standard bubbles near blow-up points for these equations.

Findings

Sharp estimates on solution differences near blow-up points

Characterization of bubbling solutions for fourth order equations

Insights into the structure of solutions on 4-manifolds

Abstract

We study a class of fourth order geometric equations defined on a 4-dimensional compact Riemannian manifold which includes the Q-curvature equation. We obtain sharp estimates on the difference near the blow-up points between a bubbling sequence of solutions and the standard bubble.