The Domain Geometry and the Bubbling Phenomenon of Rank Two Gauge Theory

Abstract

Let Ω be a flat torus and G be the Green’s function of - Δ on Ω. One intriguing mystery of G is how the number of its critical points is related to blowup solutions of certain PDEs. In this article we prove that for the following equation that describes a Chern–Simons model in Gauge theory:(Formula Presented.),if fully bubbling solutions of Liouville type exist, G has exactly three critical points. In addition we establish necessary conditions for the existence of fully bubbling solutions with multiple bubbles.