Geometric evolution equations in critical dimensions
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- Grotowski, J.F. & Shatah, J. Calc. Var. (2007) 30: 499. doi:10.1007/s00526-007-0100-2
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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.