Entropy, stability, and Yang-Mills flow

Casey Kelleher, Jeffrey Streets

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Following [T. Colding and W. Minicozzi, II, Generic mean curvature flow I; generic singularities, Ann. of Math. 175(2) (2012) 755-833], we define a notion of entropy for connections over ℝn which has shrinking Yang-Mills solitons as critical points. As in [T. Colding and W. Minicozzi, II, Generic mean curvature flow I; generic singularities, Ann. of Math. 175(2) (2012) 755-833], this entropy is defined implicitly, making it difficult to work with analytically. We prove a theorem characterizing entropy stability in terms of the spectrum of a certain linear operator associated to the soliton. This leads furthermore to a gap theorem for solitons. These results point to a broader strategy of studying "generic singularities" of the Yang-Mills flow, and we discuss the differences in this strategy in dimension n = 4 versus n ≥ 5.

Original languageEnglish (US)
Article number1550032
JournalCommunications in Contemporary Mathematics
Volume18
Issue number2
DOIs
StatePublished - Apr 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Yang-Mills
  • entropy
  • geometric flow
  • stability

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