Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-18T06:11:21.585Z Has data issue: false hasContentIssue false
  • English
  • Français

Global solution for the Yang-Mills gradient flow on 4-manifolds

Published online by Cambridge University Press:  22 January 2016

Hideo Kozono ,
Yoshiaki Maeda  and
Hisashi Naito
Hideo Kozono
Affiliation:
Graduate School of Polymathematics, Nagoya University, Nagoya, 464-01, Japan
Yoshiaki Maeda
Affiliation:
Department of Mathematics, Faculty of Science and Technology, Keio University, Yokohama, 223, Japan The Erwin Schrödinger International, Institute for Mathematical Physics, Wien, A-1090, Austria
Hisashi Naito
Affiliation:
Graduate School of Polymathematics, Nagoya University, Nagoya, 464-01, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we will study a global weak solution for the Yang-Mills gradient flow on a closed (i.e., compact without boundary) 4-manifold. Let us explain some notion briefly to be able to state our results.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 139 , September 1995 , pp. 93 - 128
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1995

References

[ 1 ] Fujiwara, D., On the asymptotic behaviour of the Green operators for elliptic boundary problems and the pure imaginary powers of the second order operators, J. Math. Soc. Japan, 21 (1969), 481–521.Google Scholar
[ 2 ] Jost, J., “Nonlinear Methods in Riemannian and Kählerian Geometry,” Birkhäuser, Basel, 1988.Google Scholar
[ 3 ] Kono, K. and Nagasawa, T., Weak asymptotic stability of Yang-Mills gradient flow, Tokyo J. Math., 11 (1988), 339–357.Google Scholar
[ 4 ] Ladyzenskaja, O. A., Solonnikov, V. A. and Ural’ceva, N. N., “Linear and Quasilinear Equations of Parabolic Type,” American Mathematical Society, Providence, 1968.CrossRefGoogle Scholar
[ 5 ] Moser, J., A Harnack inequality for parabolic differential equations, Commun. Pure and Apply. Math., 17 (1964), 101–134.CrossRefGoogle Scholar
[ 6 ] Nagasawa, T., Asymptotic stability of Yang-Mills’ gradient flow, in “Geometry of Manifolds (edited by K. Shiohama),” Academic Press, Boston, 1989, pp. 499–517.Google Scholar
[ 7 ] Naito, H., Kozono, H. and Maeda, Y., A stable manifold theorem for the Yang-Mills gradient flow, Tôhoku Math. J., 42 (1990), 45–66.CrossRefGoogle Scholar
[ 8 ] Sedlacek, S., A direct method for minimizing the Yang-Mills functional over 4-manifolds, Commun. Math. Phys., 86 (1982), 515–527.CrossRefGoogle Scholar
[ 9 ] Struwe, M., On the evolution of harmonic mappings of Riemann surfaces, Comm. Math. Helv., 4 (1985), 558–581.Google Scholar
[10] Tanabe, H., “Equation of Evolution,” Pitmann, London, 1979.Google Scholar
[11] Temam, R., “Naviar-Stokes equations, theory and numerical analysis,” North-Holland, Amsterdam-New York-Oxford, 1979.Google Scholar
[12] Uhlenbeck, K., Removable singularities in Yang-Mills fields, Commun. Math. Phys., 83 (1982), 11–29.CrossRefGoogle Scholar
[13] Uhlenbeck, K., Connections with L -bounds on curvature, Commun. Math. Phys., 83 (1982), 31–42.Google Scholar