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 language||English (US)|
|Number of pages||14|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - Dec 2007|
ASJC Scopus subject areas
- Applied Mathematics