arXiv research

We prove the first mathematical result relating the Yang-Mills measure on a compact surface and the Yang-Mills energy. We show that, at the small volume limit, the Yang-Mills measures satisfy a large deviation principle with a rate function which is expressed in a simple and natural way in terms of the Yang-Mills energ…

Study bounds the index of minimal submanifolds using energy measures and Yang-Mills-Higgs equations.

New approach to Yang-Mills measure on surfaces via Morse theory.

A new state-sum formula for the evaluation of the Yang-Mills measure in the Kauffman bracket skein algebra of a closed surface is derived. The formula extends the Kauffman bracket to diagrams that lie in surfaces other than the plane. It also extends Turaev's shadow world invariant of links in a circle bundle over a su…

Researchers can retrieve Yang-Mills-Higgs fields from Minkowski space measurements.

Utilizing a number of results of Dittmann, we investigate the nature of the Yang-Mills field over the eight-dimensional convex set, endowed with the Bures metric, of three-level quantum systems. Adopting a numerical strategy, we first decompose the field into self-dual and anti-self-dual components, by implementing the…

We study singularity structure of Yang-Mills flow in dimensions $n \geq 4$. First we obtain a description of the singular set in terms of concentration for a localized entropy quantity, which leads to an estimate of its Hausdorff dimension. We develop a theory of tangent measures for the flow, which leads to a stratifi…

Smooth Yang-Mills fields proved in supercritical dimensions.

Stability of singularity formation in Yang-Mills fields in higher dimensions.

Paper extends Simons theorem to $F$-Yang-Mills connections for instability.

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 integral currents used for the classical Plateau problem. The space A_{G} can be also…

Study vortices in Kähler-Yang-Mills equations on complex manifolds.

The paper studies stability of F-Yang-Mills connections on complex projective spaces.

The paper examines Yang-Mills-Higgs pairs on vector bundles and proves stability and energy identity.

Removes singularities for Yang-Mills-Higgs fields in higher dimensions.

In this paper, we introduce some notions on the pair consisting of a Chern connection and a Higgs field closely related to the first and second variation of Yang-Mills- Higgs functional, such as strong Yang-Mills-Higgs pair, degenerate Yang-Mills-Higgs pair, stable Yang-Mills-Higgs pair. We investigate some properties …

Compactifies moduli spaces of Hermitian-Yang-Mills connections on balanced manifolds.

We prove that the Yang-Mills $α$-functional satisfies the Palais-Smale condition. This guarantees the existence of critical points, which are called Yang-Mills $α$-connections. It was shown by Hong, Tian and Yin in [10] (to appear in Comm. Math. Helv.) that as $α\to 1$, a sequence of Yang-Mills $α$-connections converge…

Compact formulas for Yang-Mills conditions on conformal manifolds.

New energy functional and fields for Yang-Mills theory, proving monotonicity and vanishing theorems.

For each closed, orientable surface F, we construct a local, diffeomorphism invariant trace on the Kauffman bracket skein module K_t(F x [0,1]). The trace is defined when |t| is neither 0 nor 1, and at certain roots of unity. At t = - 1, the trace is integration against the symplectic measure on the SU(2) character var…

The paper defines and studies new types of submanifolds in a unit sphere.

We use the Yang-Mills gradient flow on the space of connections over a closed Riemann surface to construct a Morse-Bott chain complex. The chain groups are generated by Yang-Mills connections. The boundary operator is defined by counting the elements of appropriately defined moduli spaces of Yang-Mills gradient flow li…

We consider the problem of identifying a unitary Yang-Mills connection $\nabla$ on a Hermitian vector bundle from the Dirichlet-to-Neumann (DN) map of the connection Laplacian $\nabla^*\nabla$ over compact Riemannian manifolds with boundary. We establish uniqueness of the connection up to a gauge equivalence in the cas…

Explains a 1978 construction for Yang-Mills instantons.

Extends weak continuity of Yang-Mills connections to a broader class.

Study resolves conjectures on hypercritical deformed Hermitian-Yang-Mills equation.

Study on Yang-Mills equations on conformally compact manifolds, finding obstructions and asymptotics.

Study the deformation theory of Einstein-Yang-Mills system on compact manifolds.

Flat Yang-Mills connections on pinched manifolds.

Study proves uniqueness of Yang-Mills field tangent cones in arbitrary dimensions.

Study Yang-Mills connections on conformally compact manifolds, proving existence of extensions.

The paper constructs examples of coupled Dirac-Yang-Mills pairs on Riemannian manifolds.

Study on a deformed Hermitian-Yang-Mills equation on compact Kähler manifolds.

Paper proves no stable Yang-Mills fields on spheres.

Study on hermitian Yang-Mills connections on blown-up manifolds.

A local monotonicity formula for the Yang-Mills-Higgs flow on $G$-bundles over $\mathbb{R}^{n}$ ($n>4$) is proved. It is shown that the monotone quantity coïncides on certain self-similar solutions with that appearing in existing non-local monotonicity formulæ for the Yang-Mills and Yang-Mills-Higgs flows.

Proves existence of Yang-Mills fields for specific curvature conditions.

The paper studies decay near singularities of 3d Yang-Mills-Higgs fields.

The paper finds asymmetric Type-I blowup solutions for Yang-Mills flow.

Stable solutions to Yang-Mills-Higgs equations on spheres and tori identified.

In this note we introduce a Yang-Mills bar equation on complex vector bundles over compact Hermitian manifolds as the Euler-Lagrange equation for a Yang-Mills bar functional. We show the existence of a non-trivial solution of this equation over compact Kähler manifolds as well as a short time existence of the negative …

Introduces a new Yang-Mills functional for connections and scalars over circle bundles.

Let $P$ be a principal U(1)-bundle over a closed manifold $M$. On $P$, one can define a modified version of the Ricci flow called the Ricci Yang-Mills flow, due to these equations being a coupling of Ricci flow and the Yang-Mills heat flow. We use maximal regularity theory and ideas of Simonett concerning the asymptoti…

Paper proves solutions for deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds.

Example found of non-conical Hermitian Yang-Mills connection.

We construct Yang-Mills connections on SO(n)-bundles over spheres equipped with the Euclidean metric. We use a cohomogeneity one group action on the bundle to reduce the Yang-Mills-equation to a system of ordinary differential equations. The system is shown to have solutions by variational methods, using ideas from har…

We proved a uniqueness theorem of tangent connections for a Yang-Mills connection with an isolated singularity with a quadratic growth of the curvature at the singularity. We also obtained controls over the rate of the asymptotic convergence of the connection to the tangent connection under assumptions that the connect…