TY - JOUR
T1 - Higher order Yang–Mills flow
AU - Kelleher, Casey
N1 - Funding Information:
The author gratefully acknowledges her support from an NSF Graduate Research Fellowship (DGE-1321846).
Funding Information:
Acknowledgements The author would like to thank Jeffrey Streets for his unwavering support and encouragement, thoughtful advising and patient instruction. Additionally the author gratefully acknowledges support from the Simons Center for Geometry and Physics, Stony Brook University at which some of the research for this paper was performed. The author would like to thank the referee for their careful reading of the manuscript. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1321846. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - We define a family of functionals generalizing the Yang–Mills functional. We study the corresponding gradient flows and prove long-time existence and convergence results for subcritical dimensions as well as a bubbling criterion for critical dimensions. Consequently, we generalize the results of the convergence of Yang–Mills flow in dimensions 2 and 3 given by Råde (J Reine Angew Math 431:123–163, 1992) and the bubbling criterion in dimension 4 of Struwe (Calc Var 2:123–150, 1994) in the case where the initial flow data is smooth.
AB - We define a family of functionals generalizing the Yang–Mills functional. We study the corresponding gradient flows and prove long-time existence and convergence results for subcritical dimensions as well as a bubbling criterion for critical dimensions. Consequently, we generalize the results of the convergence of Yang–Mills flow in dimensions 2 and 3 given by Råde (J Reine Angew Math 431:123–163, 1992) and the bubbling criterion in dimension 4 of Struwe (Calc Var 2:123–150, 1994) in the case where the initial flow data is smooth.
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U2 - 10.1007/s00526-019-1548-6
DO - 10.1007/s00526-019-1548-6
M3 - Article
AN - SCOPUS:85065902878
SN - 0944-2669
VL - 58
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 3
M1 - 100
ER -