## 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 language | English (US) |
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Article number | 1550032 |

Journal | Communications in Contemporary Mathematics |

Volume | 18 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2016 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

## Keywords

- Yang-Mills
- entropy
- geometric flow
- stability