Journal ArticleDOI
Connections with l**p bounds on curvature
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TLDR
In this paper, it was shown by means of the implicit function theorem that Coulomb gauges exist for fields over a ball over compact manifolds when the integral field norm is sufficiently small.Abstract:
We show by means of the implicit function theorem that Coulomb gauges exist for fields over a ball inR
n
when the integralL
n/2 field norm is sufficiently small. We then are able to prove a weak compactness theorem for fields on compact manifolds withL
p
integral norms bounded,p>n/2.read more
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Journal ArticleDOI
Topological quantum field theory
TL;DR: A twisted version of four dimensional supersymmetric gauge theory is formulated in this paper, which refines a nonrelativistic treatment by Atiyah and appears to underlie many recent developments in topology of low dimensional manifolds; the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally.
Journal ArticleDOI
The Yang-Mills equations over Riemann surfaces
Michael Atiyah,Raoul Bott +1 more
TL;DR: In this article, the Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory, and the main result is that this is a perfect 9 functional provided due account is taken of its gauge symmetry.
Journal ArticleDOI
The self-duality equations on a riemann surface
TL;DR: In this paper, the authors studied a special class of solutions of the self-dual Yang-Mills equations on Riemann surfaces and showed that the moduli space of all solutions turns out to be a manifold with an extremely rich geometric structure.
Journal ArticleDOI
Anti Self‐Dual Yang‐Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles
TL;DR: In this paper, a correspondance entre the geometries algebrique and the geometry differentielle des fibres vectoriels is presented, and a connexion irreductible d'Hermite-Einstein par rapport a metrique ω.
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Higgs bundles and local systems
TL;DR: In this paper, the authors implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php).
References
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BookDOI
Multiple integrals in the calculus of variations
TL;DR: In this paper, a variational method in the theory of harmonic integrals has been proposed to solve the -Neumann problem on strongly pseudo-convex manifolds and parametric Integrals two-dimensional problems.
Book
The Topology of Fibre Bundles.
TL;DR: In this paper, a succint introduction to fiber bundles is provided, which includes such topics as differentiable manifolds and covering spaces, and a brief survey of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles.
Book
Harmonic Maps of Manifolds with Boundary
TL;DR: In this article, the heat equation for manifolds and growth estimates and convergence of growth estimates are discussed.Harmonic maps, function spaces, Semi-elliptic and parabolic equations, and heat equation are presented.