Compactness theorems for SL(2;C) generalizations of the 4-dimensional anti-self dual equations, Part II

TL;DR

This paper establishes compactness theorems for sequences of solutions to SL(2;C) analogs of anti-self dual equations on 4-manifolds, focusing on characterizing the singularities in the limits.

Contribution

It provides new compactness results and characterizations of singular loci for solutions to SL(2;C) anti-self dual equations, extending previous work.

Findings

Characterization of the singular locus in solution limits

Proof of compactness theorems for solution sequences

Analysis of the behavior of solutions near singularities

Abstract

This is the second of two papers that describe a compactness theorem for sequences of solutions of certain SL(2;C) analogs of the anti-self dual equations on oriented, 4-dimensional Riemannian manifolds. This paper proves theorems that characterize the singular locus of limits of sequences of solutions to the equations.