TY - JOUR
T1 - Geometric evolution equations in critical dimensions
AU - Grotowski, Joseph F.
AU - Shatah, Jalal
PY - 2007/12
Y1 - 2007/12
N2 - 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.
AB - 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.
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U2 - 10.1007/s00526-007-0100-2
DO - 10.1007/s00526-007-0100-2
M3 - Article
AN - SCOPUS:34548070998
SN - 0944-2669
VL - 30
SP - 499
EP - 512
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 4
ER -