×

zbMATH — the first resource for mathematics

A direct method for minimizing the Yang-Mills functional over 4- manifolds. (English) Zbl 0506.53016

MSC:
53C05 Connections (general theory)
53C80 Applications of global differential geometry to the sciences
55R40 Homology of classifying spaces and characteristic classes in algebraic topology
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Atiyah, M., Bott, R.: On the Yang-Mills Equations over Riemann surfaces (preprint) · Zbl 0509.14014
[2] Dold, A., Whitney, H.: Classification of oriented sphere bundles over a 4-complex. Ann. Math.69, 667-677 (1959) · Zbl 0124.38103
[3] Greub, W., Petry, H.: On the lifting of structure groups, in differential geometrical methods in mathematical physics II. In: Bleuler, Petry, Reetz (eds.). Lecture Notes in Mathematics, Vol. 616. Berlin, Heidelberg, New York: Springer 1968, 217-246
[4] Hartshorne, R.: Algebraic geometry. Berlin, Heidelberg, New York: Springer 1977 · Zbl 0367.14001
[5] Jaffe, A., Taubes, C.: Vortices and monopoles. Boston: Birkh?user 1980 · Zbl 0457.53034
[6] Lemaire, L.: Applications harmoniques de surfaces Riemanniennes. J. Diff. Geo.13, 51-78 (1978) · Zbl 0388.58003
[7] Morrey, C.: Multiple integrals in the calculus of variations. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0142.38701
[8] Palais, R.: Foundations of global non-linear analysis. New York: Benjamin 1968 · Zbl 0164.11102
[9] Parker, T.: Gauge theories on four dimensional Riemannian manifolds. Ph. D. thesis, Stanford University (1980) · Zbl 0502.53022
[10] Sacks, J., Uhlenbeck, K.: The existence of minimal immersions of 2-spheres. Ann. Math.113, 1-24 (1981) · Zbl 0462.58014
[11] Samelson, H.: Topology of Lie groups. Bull. Am. Math. Soc.58, 2-37 (1952) · Zbl 0047.16701
[12] Schoen, R., Yau, S.-T.: Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature. Ann. Math.110, 127-142 (1979) · Zbl 0431.53051
[13] Taubes, C.: Self-dual Yang-Mills connections on non-self dual 4-manifolds (to appear) · Zbl 0484.53026
[14] t’ Hooft, G.: Some twisted self-dual solutions for the Yang-Mills equations on a hypertorus. Commun. Math. Phys.81, 267-275 (1981) · Zbl 0475.35075
[15] Uhlenbeck, K.: Connections withL p bounds on curvature. Commun. Math. Phys.83, 31-42 (1982) · Zbl 0499.58019
[16] Uhlenbeck, K.: Removable singularities in Yang-Mills fields. Commun. Math. Phys.83, 11-30 (1982) · Zbl 0491.58032
[17] Uhlenbeck, K.: Variational problems for gauge fields, annals studies. Proceddings of Special Year in Diff. Geometry, Institute for Advanced Study (1980)
[18] Warner, F.: Foundations of differentiable manifolds and Lie groups. Illinois: Scott, Foresman and Company, 1971
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.