Related papers: Compactness for $\Omega$-Yang-Mills connections

The main goal of this paper is to generalize a part of the relationship between mean curvature and Harder-Narasimhan filtrations of holomorphic vector bundles to arbitrary polarized fibrations. More precisely, for a polarized family of…

On conformally compact manifolds we study Yang-Mills equations, their boundary conditions, formal asymptotics, and Dirichlet-to-Neumann maps. We find that smooth solutions with "magnetic" Dirichlet boundary data are obstructed by a…

We formalize the ``metric bundle'' viewpoint by defining, for any smooth $n$--manifold $M$, the open fiberwise cones $\mathcal{G}^{p,q}\subset S^2\Tstar M$ of nondegenerate symmetric bilinear forms with fixed signature $(p,q)$, and we…

Given a compact K\"ahler manifold $X$, there is an equivalence of categories between the completely reducible flat vector bundles on $X$ and the polystable Higgs bundles $(E,\, \theta)$ on $X$ with $c_1(E)= 0= c_2(E)$ \cite{SimC},…

We write down the weak-coupling limit of N=2 supersymmetric Yang-Mills theory with arbitrary gauge group \( G \). We find the weak-coupling monodromies represented in terms of \( Sp(2r,\bzeta ) \) matrices depending on paths closed up to…

We prove that if an N-vortex pair nearly minimizes the Yang-Mills-Higgs energy, then it is second order close to a minimizer. First we use new weighted inequalities in two dimensions and compactness arguments to show stability for sections…

For analyzing stationary Yang-Mills connections in higher dimensions, one has to work with Morrey-Sobolev bundles and connections. The transition maps for a Morrey-Sobolev principal $G$-bundles are not continuous and thus the usual notion…

In this article we discuss the geometry of moduli spaces of (1) flat bundles over special Lagrangian submanifolds and (2) deformed Hermitian-Yang-Mills bundles over complex submanifolds in Calabi-Yau manifolds. These moduli spaces reflect…

This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such…

T. Riviere proved an energy quantization for Yang-Mills fields defined on n-dimensional Riemannian manifolds, when $n$ is larger than the critical dimension 4. More precisely, he proved that the defect measure of a weakly converging…

We classify four-dimensional connected simply-connected indecomposable Lorentzian symmetric spaces $M$ with connected nontrivial isotropy group furnishing solutions of the Einstein-Yang-Mills equations. Those solutions with respect to some…

The main result of this article provides a characterization of reductive homogeneous spaces equipped with some geometric structure (non necessarily pseudo-Riemannian) in terms of the existence of certain connection. The result generalizes…

In arXiv:0805.2192, we set up a gauge-theoretic equation on symplectic 6-manifolds, which is a version of the Hermitian-Einstein equation perturbed by Higgs fields, and call Donaldson-Thomas equation, to analytically approach the…

Let $Y$ be a CW-complex with a single 0-cell, let $K$ be its Kan group, a free simplicial group whose realization is a model for the space $\Omega Y$ of based loops on $Y$, and let $G$ be a Lie group, not necessarily connected. By means of…

This paper develops Yang-Mills flow on Riemannian manifolds with special holonomy. By analogy with the second-named author's thesis, we find that a supremum bound on a certain curvature component is sufficient to rule out finite-time…

In this paper we prove weak L^{1,p} (and thus C^{\alpha}) compactness for the class of uniformly mean-convex Riemannian n-manifolds with boundary satisfying bounds on curvature quantities, diameter, and (n-1)-volume of the boundary. We…

The purpose of this paper is to exhibit a natural construction between complex geometry and symplectic geometry following the idea of mirror symmetry. Suppose we are given a family of pairs of 2-dimensional K\"ahler tori and stable…

Exploiting the formulation of the Self Dual Yang-Mills equations as a Riemann-Hilbert factorization problem, we present a theory of pulling back soliton hierarchies to the Self Dual Yang-Mills equations. We show that for each map $ \C^4 \to…

We prove that the Yang-Mills (YM) measure for the trivial principal bundle over the two-dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a…

We observe that the main feature of the Randall-Sundrum model, used to solve the hierarchy problem, is already present in a class of Yang-Mills plus gravity theories inspired by noncommutative geometry. Strikingly the same expression for…