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

Hsin-Yuan Huang; Lei Zhang

doi:10.1007/s00220-016-2685-9

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

Hsin-Yuan Huang ^*, Lei Zhang

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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	https://doi.org/10.1007/s00220-016-2685-9
State	Published - 1 Jan 2017

Access to Document

10.1007/s00220-016-2685-9

Fingerprint Dive into the research topics of 'The Domain Geometry and the Bubbling Phenomenon of Rank Two Gauge Theory'. Together they form a unique fingerprint.

Cite this

@article{965419138d0644468ae844dbec0a3c92,

title = "The Domain Geometry and the Bubbling Phenomenon of Rank Two Gauge Theory",

abstract = "Let Ω be a flat torus and G be the Green{\textquoteright}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.",

author = "Hsin-Yuan Huang and Lei Zhang",

year = "2017",

month = jan,

day = "1",

doi = "10.1007/s00220-016-2685-9",

language = "English",

volume = "349",

pages = "393--424",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - The Domain Geometry and the Bubbling Phenomenon of Rank Two Gauge Theory

AU - Huang , Hsin-Yuan

AU - Zhang, Lei

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84974831645&partnerID=8YFLogxK

U2 - 10.1007/s00220-016-2685-9

DO - 10.1007/s00220-016-2685-9

M3 - Article

AN - SCOPUS:84974831645

VL - 349

SP - 393

EP - 424

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -