Some boundedness properties of solutions to the complex Yang-Mills equations on closed 4-manifolds

被引：0

作者：

Huang, Teng ^{[1
,2
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Peoples R China

[2] Chinese Acad Sci, Key Lab Wu Wen Tsun Math, Hefei 230026, Peoples R China

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2020年 / 68卷

基金：

中国国家自然科学基金;

关键词：

Complex Yang-Mills equations; Kapustin-Witten equations; Gauge theory; ENERGY-GAP; CONNECTIONS; DUALITY;

D O I：

10.1016/j.difgeo.2019.101563

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study the analytical properties of the solutions of the complex Yang-Mills equations on a closed Riemannian four-manifold X with a Riemannian metric g. The main result is that if g is good and the connection is an approximate ASD connection, then the extra field has a positive lower bound. As an application, we obtain some gap results for Yang-Mills connections and Kapustin-Witten equations. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：19

共 21 条

[1] STABILITY AND ISOLATION PHENOMENA FOR YANG-MILLS FIELDS
BOURGUIGNON, JP
LAWSON, HB
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1981, 79 (02) : 189 - 230
[2] Chavel I, 1984, PURE APPL MATH, V115
[3] Donaldson S.K., 1993, GEOM FUNCT ANAL, V3, P179
[4] Donaldson S. K., 1990, GEOMETRY 4 MANIFOLDS
[5] Donaldson S. K., 2002, Cambridge Tracts in Mathematics, V147
[6] Feehan P.M.N., ARXIVMATH9812060V3
[7] Feehan P.M.N., ARXIV14091525
[8] Energy gap for Yang-Mills connections, II: Arbitrary closed Riemannian manifolds
Feehan, Paul M. N.
[J]. ADVANCES IN MATHEMATICS, 2017, 312 : 547 - 587
[9] Energy gap for Yang-Mills connections, I: Four-dimensional closed Riemannian manifolds
Feehan, Paul M. N.
[J]. ADVANCES IN MATHEMATICS, 2016, 296 : 55 - 84
[10] Critical-exponent Sobolev norms and the slice theorem for the quotient space of connections
Feehan, PMN
[J]. PACIFIC JOURNAL OF MATHEMATICS, 2001, 200 (01) : 71 - 118

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