arXiv research

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

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

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

Flat Yang-Mills connections on pinched 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…

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

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

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

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 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…

Compact formulas for Yang-Mills conditions on conformal manifolds.

Study classifies Einstein-Yang-Mills spaces in 4D symmetric spaces.

Study extends Yang-Mills energy gap to Kähler surfaces.

Characterizes tangent cones for specific connections on reflexive sheaves.

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…

Stability of Yang-Mills connections' Morse indices and nullity in 4D.

We construct the most general reducible connection that satisfies the self-dual Yang-Mills equations on a simply connected, open subset of flat $\mathbb{R}^4$. We show how all such connections lie in the orbit of the flat connection on $\mathbb{R}^4$ under the action of non-local symmetries of the self-dual Yang-Mills …

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 …

Direct method finds Yang-Mills connections for SO(3) bundles.

Study hermitian Yang-Mills connections on pullback bundles for holomorphic submersions.

Smooth Yang-Mills fields proved in supercritical dimensions.

The study finds a positive lower bound for the extra field in Yang-Mills equations on closed 4-manifolds.

We generalize our previous results (Theorem 1 and Corollary 2 in arXiv:1412.4114) and Theorem 1 in arXiv:1502.00668) on the existence of an $L^2$-energy gap for Yang-Mills connections over closed four-dimensional manifolds and energies near the ground state (occupied by flat, anti-self-dual, or self-dual connections) t…

Working over a pseudo-Riemannian manifold, for each vector bundle with connection we construct a sequence of three differential operators which is a complex (termed a Yang-Mills detour complex) if and only if the connection satisfies the full Yang-Mills equations. A special case is a complex controlling the deformation…

Study on Yang-Mills fields blow-up in 4D, proving certain configurations impossible.

Vortices and coupled vortices arise from Yang-Mills-Higgs theories and can be viewed as generalizations or analogues to Yang-Mills connections and, in particular, Hermitian-Yang-Mills connections. We proved an analytic compactification of the moduli spaces of vortices and coupled vortices on hermitian vector bundles ov…

Paper proves no stable Yang-Mills fields on spheres.

Study on HYM connections on Kähler manifolds, calculating moduli space virtual dimension.

We consider the minimum Yang-Mills energy on the complete $G_{2}$-manifolds and Calabi-Yau 3-folds,the connection $A$ is a stability Yang-Mills connection on the $G$-bundle $E$.We prove that the connection must be a $G_{2}$-instanton on $G_{2}$-manifold and the bundle is holomorphic on Calabi-Yau 3-fold with holonomy $…

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

Given a principal bundle on an orientable closed surface with compact connected structure group, we endow the space of based gauge equivalence classes of smooth connections relative to smooth based gauge transformations with the structure of a Fréchet manifold. Using Wilson loop holonomies and a certain characteristic …

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

We study the problem of finding good gauges for connections in higher gauge theories. We find that, for $2$-connections in strict $2$-gauge theory and $3$-connections in $3$-gauge theory, there are local "Coulomb gauges" that are more canonical than in classical gauge theory. In particular, they are essentially unique,…

Develops equivariant connections for Yang-Mills equations, simplifying interactions modeling.

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

Study Yang-Mills connections on four-manifolds, derive obstructions to bubbling.

Explains a 1978 construction for Yang-Mills instantons.

In the spirit of recent work of Lamm, Malchiodi and Micallef in the setting of harmonic maps, we identify Yang-Mills connections obtained by approximations with respect to the Yang-Mills α-energy. More specifically, we show that for the SU(2) Hopf fibration over the four sphere, for sufficiently small α values the SO(4…

We prove that Yang-Mills connections on a surface are characterized as those with the property that the holonomy around homotopic closed paths only depends on the oriented area between the paths. Using this we have an alternative proof for a theorem of Atiyah and Bott that the Yang-Mills connections on a compact orient…

New examples of deformed Hermitian-Yang-Mills connections found.

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 …

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

If we consider the moduli space of flat connections of a non trivial principal SO(3)-bundle over a surface, then we can define a map from the set of perturbed closed geodesics, below a given energy level, into families of perturbed Yang-Mills connections depending on a small parameter. In this paper we show that this m…

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

We study Yang-Mills connections on holomorphic bundles over complex Kähler manifolds of arbitrary dimension, in the spirit of Hitchin's and Simpson's study of flat connections. The space of non-Hermitian Yang-Mills (NHYM) connections has dimension twice the space of Hermitian Yang-Mills connections, and is locally isom…

Extends Yang-Mills theory to non-integrable Lie algebroids.

Let $Σ$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $ξ\colon P \to Σ$ be a principal $G$-bundle, and pick a Riemannian metric and orientation on $Σ$ so that the corresponding Yang-Mills equations are defined.…

In "The Yang-Mills equations over Riemann surfaces", Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. We generalize their study to all closed, compact, connected, possibly nonorientable surfaces. We introduce the notion of "super central extension" of the fund…