Geometric evolution equations in critical dimensions

Grotowski, J. F. and Shatah, J. (2007) Geometric evolution equations in critical dimensions. Calculus of Variations and Partial Differential Equations, 30 4: 499-512. doi:10.1007/s00526-007-0100-2

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Author Grotowski, J. F.
Shatah, J.
Title Geometric evolution equations in critical dimensions
Journal name Calculus of Variations and Partial Differential Equations   Check publisher's open access policy
ISSN 0944-2669
Publication date 2007
Sub-type Article (original research)
DOI 10.1007/s00526-007-0100-2
Volume 30
Issue 4
Start page 499
End page 512
Total pages 14
Editor L Ambrosio
G. Huisken
A. Malchiodi
Place of publication Berlin, Germany
Publisher Springer
Collection year 2008
Language eng
Subject 230107 Differential, Difference and Integral Equations
780101 Mathematical sciences
010110 Partial Differential Equations
010102 Algebraic and Differential Geometry
0101 Pure Mathematics
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.
Keyword Geometric flows
Yang-Mills heat flow
Harmonic map heat flow
Q-Index Code C1

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Created: Wed, 02 Apr 2008, 12:26:05 EST by Marie Grove on behalf of School of Mathematics & Physics