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.
Original language | English |
---|---|
Pages (from-to) | 393-424 |
Number of pages | 32 |
Journal | Communications in Mathematical Physics |
Volume | 349 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2017 |