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Uhlenbeck, Karen K.

Removable singularities in Yang-Mills fields. (English) Zbl 0491.58032

Commun. Math. Phys. 83, 11-29 (1982).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 9 Reviews
Cited in 192 Documents

MSC:

58J90 Applications of PDEs on manifolds
53C80 Applications of global differential geometry to the sciences
81T08 Constructive quantum field theory
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory

Keywords:

Yang-Mills equations for trivial bundles over flat manifolds and compact structure group in dimension 4 with a point singularity; gauge equivalent to a smooth field; Yang-Mills field with bounded functional; Hodge gauges; Coulomb gauges
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References:

[1] Atiyah, M. F.: Geometry of Yang-Mills fields, Lezioni Fermi, Accademia Nazionale Dei Lincei Scuola Normale Superiore, Pisa (1979) · Zbl 0435.58001
[2] Atiyah, M. F. Bott, R.: On the Yang-Mills equations over Riemann surfaces (Preprint) · Zbl 0509.14014
[3] Atiyah, M. F. Hitchen, N. Singer, I.: Proc. R. Soc. London A362, 425–461 (1978) · Zbl 0389.53011 · doi:10.1098/rspa.1978.0143
[4] Bourguignon, J. P. Lawson, H. B.: Yang-Mills theory: Its physical origins and differential geometric aspects (Preprint) · Zbl 0482.58007
[5] Bourguignon, J. P. Lawson, H. B.: Commun. Math. Phys.79, 189–203 (1981) · Zbl 0475.53060 · doi:10.1007/BF01942061
[6] Gidas B.: Euclidean Yang-Mills and related equations, Bifurcation Phenomena in Mathematical Physics and Related Topics pp. 243–267 Dordrecht: Reidel Publishing Co. 1980
[7] Hildebrandt, S., Kaul, H., Widman, K.-O.: Acta Math.138, 1–16 (1977) · Zbl 0356.53015 · doi:10.1007/BF02392311
[8] Jaffe, A. Taubes, C.: Vortices and monopoles. Progress in Physics 2. Boston: Birkhäuser 1980 · Zbl 0457.53034
[9] Morrey, C. B.: Multiple integrals in the calculus of variations. New York: Springer 1966 · Zbl 0142.38701
[10] Parker, T.: Gauge theories on four dimensional manifolds. Ph.D. Thesis, Stanford (1980)
[11] Ray, D.: Adv. Math.4, 111–126 (1970) · Zbl 0204.23804 · doi:10.1016/0001-8708(70)90018-6
[12] Sacks, J. Uhlenbeck, K.: The existence of minimal two-spheres. Ann. Math. (to appear) · Zbl 0375.49016
[13] Sibner, L. M.: (private communication)
[14] Taubes, C.: The Existence of Multi-Monopole Solutions to the Non-Abelian, Yang-Mills-Higgs Equations for Arbitrary Simple Gauge Groups. Commun. Math. Phys. (to appear) · Zbl 0486.35072
[15] Uhlenbeck, K.: Bull. Am. Math. Soc.1, (New Series) 579–581 (1979) · Zbl 0416.35026 · doi:10.1090/S0273-0979-1979-14632-9
[16] Uhlenbeck, K.: Connections withL bounds on curvature. Commun. Math. Phys.83, 31–42 (1982) · Zbl 0499.58019 · doi:10.1007/BF01947069
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