Geometric evolution equations in critical dimensions

Joseph F. Grotowski, Jalal Shatah

Research output: Contribution to journalArticlepeer-review

Abstract

We make a qualitative comparison of phenomena occurring in two different geometric flows: the harmonic map heat flow in two space dimensions and the Yang-Mills heat flow in four space dimensions. Our results are a regularity result for the degree-2 equivariant harmonic map flow, and a blow-up result for an equivariant Yang-Mills-like flow. The results show that qualitatively differing behaviours observed in the two flows can be attributed to the degree of the equivariance.

Original languageEnglish (US)
Pages (from-to)499-512
Number of pages14
JournalCalculus of Variations and Partial Differential Equations
Volume30
Issue number4
DOIs
StatePublished - Dec 2007

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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