Energy identity for stationary Yang Mills
成果类型：
Article
署名作者：
Naber, Aaron; Valtorta, Daniele
署名单位：
Northwestern University; University of Zurich
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-019-00854-9
发表日期：
2019
页码：
847-925
关键词：
摘要：
Given a principal bundle PM over a Riemannian manifold with compact structure group G, let us consider a stationary Yang-Mills connection A with energy M|FA|2. If we consider a sequence of such connections Ai, then it is understood by Tian (Ann Math 151(1):193-268, 2000) that up to subsequence we can converge AiA to a singular limit connection such that the energy measures converge |FAi|2dvg|FA|2dvg+, where =e(x)dn-4 is the n-4 rectifiable defect measure. Our main result is to show, without additional assumptions, that for n-4 a.e. point the energy density e(x) may be computed explicitly as the sum of the bubble energies arising from blow ups at x. Each of these bubbles may be realized as a Yang Mills connection over S4 itself. This energy quantization was proved in Riviere (Commun Anal Geom 10(4):683-708, 2002) assuming a uniform L1 hessian bound on the curvatures in the sequence. In fact, our second main theorem is to show this hessian bound holds automatically. Precisely, given a connection A as above we have the a-priori estimate M|delta 2FA|