Journal ArticleDOI
Removable singularities in Yang-Mills fields
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TLDR
In this paper, it was shown that a field satisfying the Yang-Mills equations in dimension 4 with a point singularity is gauge equivalent to a smooth field if the functional is finite.Abstract:
We show that a field satisfying the Yang-Mills equations in dimension 4 with a point singularity is gauge equivalent to a smooth field if the functional is finite. We obtain the result that every Yang-Mills field overR
4 with bounded functional (L
2 norm) may be obtained from a field onS
4=R
4∪{∞}. Hodge (or Coulomb) gauges are constructed for general small fields in arbitrary dimensions including 4.read more
Citations
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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.
Journal ArticleDOI
Monopoles and four-manifolds
TL;DR: In this paper, a new viewpoint about Donaldson theory of four manifolds was proposed, where instead of defining four-manifold invariants by counting $SU(2)$ instantons, one can define equivalent four manifold invariants using solutions of a non-linear equation with an abelian gauge group, in which the gauge group is the dual of the maximal torus of the Donaldson invariant.
Journal ArticleDOI
On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
A. Bahri,Jean-Michel Coron +1 more
TL;DR: Soit Ω un ensemble ouvert borne regulier et connexe de R N, N≥3. On considere u:Ω→R telle que −Δu=u (N+2)/(N−2) dans Ω, u>0 dans ǫ, u=0 sur ∂Ω as discussed by the authors.
Posted Content
Monopoles and Four-Manifolds
TL;DR: In this paper, a new viewpoint about Donaldson theory of four manifolds was proposed, where instead of defining four-manifold invariants by counting $SU(2)$ instantons, one can define equivalent four manifold invariants using solutions of a non-linear equation with an abelian gauge group, in which the gauge group is the dual of the maximal torus of the Donaldson invariant.
Journal ArticleDOI
Instantons on Noncommutative R 4 , and (2; 0) Superconformal Six Dimensional Theory
Nikita Nekrasov,Albert Schwarz +1 more
TL;DR: In this article, it was shown that the resolution of moduli space of ideal instantons parameterizes the instantons on non-commutative ℝ4, which is the Higgs branch of the theory of k D0-branes bound to N D4-brane by the expectation value of the B field.
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.
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
Self-duality in four-dimensional Riemannian geometry
TL;DR: In this article, the authors present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis, and apply this to the self-dual Yang-Mills equations in Euclidean 4-space and compute the number of moduli for any compact gauge group.
Journal ArticleDOI
Connections with l**p bounds on curvature
TL;DR: 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.