TY - JOUR
T1 - Limits of Yang–Mills α -connections
AU - Kelleher, Casey Lynn
N1 - Funding Information:
Acknowledgements The author deeply thanks Richard Schoen for encouraging her to investigate this subject and for the many insightful and motivating conversations. She expresses sincere appreciation to Jeffrey Streets for his unwavering support. The author deeply appreciates the insight from Mark Stern, Gang Tian, and Karen Uhlenbeck, which helped significantly with her perspective on the subject and key components of the argument. She is grateful for her encouraging conversations with Tobias Lamm about his related work. The author expresses gratitude to Tristan Rivière for inviting her to work at the Forschungsinstitut für Mathematik at ETH Zürich, where she completed this work. This material is based upon work supported by a National Science Foundation Graduate Research Fellowship under Grant No. DGE-1321846. The research was supported by NSF Grant No. DMS-1440140 while the author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the spring semester in 2016. The author was supported by a University of California President’s Year Dissertation Fellowship while completing this paper.
Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/4/1
Y1 - 2019/4/1
N2 - In the spirit of recent work of Lamm, Malchiodi and Micallef in the setting of harmonic maps (Lamm et al. in Limits of α-harmonic maps, 2015), we identify Yang–Mills connections obtained by approximations with respect to the Yang–Mills α-energy. More specifically, we show that for the SU(2) Hopf fibration over S 4 , for sufficiently small α values the SO(4) invariant ADHM instanton is the unique α-critical point which has Yang–Mills α-energy lower than a specific threshold.
AB - In the spirit of recent work of Lamm, Malchiodi and Micallef in the setting of harmonic maps (Lamm et al. in Limits of α-harmonic maps, 2015), we identify Yang–Mills connections obtained by approximations with respect to the Yang–Mills α-energy. More specifically, we show that for the SU(2) Hopf fibration over S 4 , for sufficiently small α values the SO(4) invariant ADHM instanton is the unique α-critical point which has Yang–Mills α-energy lower than a specific threshold.
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U2 - 10.1007/s00526-019-1508-1
DO - 10.1007/s00526-019-1508-1
M3 - Article
AN - SCOPUS:85063469055
SN - 0944-2669
VL - 58
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 2
M1 - 76
ER -