Related papers: Energy Quantization for Yamabe's problem in Confor…

On any closed Riemannian manifold of dimension $n\geq 3$, we prove that if a function nearly minimizes the Yamabe energy, then the corresponding conformal metric is close, in a quantitative sense, to a minimizing Yamabe metric in the…

We study the minimization problem for the Yang-Mills energy under fixed boundary connection in supercritical dimension $n\geq 5$. We define the natural function space A_{G} in which to formulate this problem in analogy to the space of…

We consider a vector bundle $E$ over a compact Riemannian manifold $M$=$M^{n}$,$n\geq 4$,and $A$ is a Yang-Mills connection with $L^{\frac{n}{2}}$ curvature $F_{A}$ on $E$.Then we prove a mean value inequality for the density…

We use the energy gap result of pure Yang-Mills equation [Feehan P.M.N., Adv. Math. 312 (2017), 547-587, arXiv:1502.00668] to prove another energy gap result of complex Yang-Mills equations [Gagliardo M., Uhlenbeck K., J. Fixed Point Theory…

This paper proves a general Uhlenbeck compactness theorem for sequences of solutions of Yang-Mills flow on Riemannian manifolds of dimension $n \geq 4,$ including rectifiability of the singular set at finite or infinite time.

We establish an energy quantization for constrained Willmore surfaces, where the constraints are given by area, volume, and total mean curvature, assuming that the underlying conformal structures remain bounded. Furthermore, we show strong…

We quantize abelian Yang-Mills theory on Riemannian manifolds with boundaries in any dimension. The quantization proceeds in two steps. First, the classical theory is encoded into an axiomatic form describing solution spaces associated to…

In this paper we demonstrate that under general conditions there exists a metric in the conformal class of an arbitrary metric on a smooth, closed Riemannian manifold of dimension greater than four such that the $Q$-curvature of the metric…

We study the existence of conformal metrics on non-compact Riemannian manifolds with non-compact boundary, which are complete as metric spaces and have negative constant scalar curvature in the interior and negative constant mean curvature…

In this paper, we study the properties of the critical points of Yang-Mills-Higgs functional, which are called Yang-Mills-Higgs pairs. We first consider the properties of weakly stable Yang-Mills-Higgs pairs on a vector bundle over S^n (n >…

Consider a Yang-Mills connection over a Riemann manifold $M=M^n$, $n\ge 3$, where $M$ may be compact or complete. Then its energy must be bounded from below by some positive constant, if $M$ satisfies certain conditions, unless the…

Given a principal bundle $P\to M$ over a Riemannian manifold with compact structure group $G$, let us consider a stationary Yang-Mills connection $A$ with energy $\int_M |F_A|^2\le \Lambda$. If we consider a sequence of such connections…

We prove that the renormalized Yang-Mills energy on six dimensional Poincar\'e-Einstein spaces can be expressed as the bulk integral of a local, pointwise conformally invariant integrand. We show that the latter agrees with the…

This paper establishes decay estimates near isolated singularities for $n$-dimensional Yang-Mills-Higgs fields defined on a fiber bundle ($n \geq 4$). These estimates yield a removable singularity theorem for Yang-Mills-Higgs fields under…

We consider the Yangs-Mills equations in 4+1 dimensions. This is the energy critical case and we show that it admits a family of solutions which blow up in finite time. They are obtained by the spherically symmetric ansatz in the SO(4)…

On a Riemannian manifold of dimension $n$ we extend the known analytic results on Yang-Mills connections to the class of connections called $\Omega$-Yang-Mills connections, where $\Omega$ is a smooth, not necessarily closed, $(n-4)$-form.…

We perform the Batalin-Vilkovisky quantization of Yang-Mills theory on a 2-point space, discussing the formulation of Connes-Lott as well as Connes' real spectral triple approach. Despite of the model's apparent simplicity the gauge…

We study five-dimensional Yang-Mills theories compactified on an S^1/Z_2 orbifold. The fundamental Lagrangian naturally includes brane kinetic terms at the orbifold fixed points which are induced by quantum corrections of the bulk fields.…

General string-theoretic considerations suggest that four-dimensional large-N gauge theories should have dual descriptions in terms of two-dimensional conformal field theories. However, for non-supersymmetric confining theories such as pure…

We consider the Abelian Yang-Mills-Higgs functional, in the non-self dual scaling, on a complex line bundle over a closed Riemannian manifold of dimension $n\geq 3$. This functional is the natural generalisation of the Ginzburg-Landau model…