Paper extends Simons theorem to F-Yang-Mills connections for instability.
problem Tackles instability of F-Yang-Mills connections. method Extends Simons theorem to F-Yang-Mills connections using Kobayashi-Ohnita-Takeuchi's method. result Derives a sufficient condition for instability of non-flat F-Yang-Mills connections. Study vortices in Kähler-Yang-Mills equations on complex manifolds.
problem Solving coupled equations for Kähler metrics and connections.
method Dimensional reductions of Kähler-Yang-Mills equations to study vortices.
result Found solutions to Yang-Mills-Higgs equations related to vortices.
The paper studies stability of F-Yang-Mills connections on complex projective spaces.
problem Stability of F-Yang-Mills connections on complex projective spaces.
method Inspired by Lawson-Simons, the paper proves stability conditions and structures for F-Yang-Mills connections.
result Conditions for weakly stable F-Yang-Mills connections on complex projective spaces.
The paper examines Yang-Mills-Higgs pairs on vector bundles and proves stability and energy identity.
problem Stability and energy identity of Yang-Mills-Higgs pairs on vector bundles.
method Bubble-neck decomposition and analysis of weakly stable pairs.
result A sequence of Yang-Mills-Higgs pairs converges to a Yang-Mills-Higgs pair with uniformly bounded energy.
Removes singularities for Yang-Mills-Higgs fields in higher dimensions.
problem Yang-Mills-Higgs fields with isolated singularities.
method Establishes decay estimates and conformally invariant energy bounds.
result Removable singularity theorem for Yang-Mills-Higgs fields.
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.
problem Analyzing Ω-Yang-Mills connections on Riemannian manifolds. method Extending known results on Yang-Mills connections to Ω-Yang-Mills connections, proving weak compactness and removable singularity theorems. result Compactification of moduli spaces of smooth Hermitian-Yang-Mills connections on unitary bundles over 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→1, a sequence of Yang-Mills α-connections converge…
Compact formulas for Yang-Mills conditions on conformal manifolds.
problem Finding variational analogs of Yang-Mills conditions.
method Provided compact formulas and proved their equivalence to Yang-Mills conditions under specific metrics.
result Conformal Yang-Mills condition is equivalent to vanishing of Fefferman-Graham obstruction tensor.
New energy functional and fields for Yang-Mills theory, proving monotonicity and vanishing theorems.
problem Developing new mathematical tools for Yang-Mills theory.
method Introducing normalized exponential Yang-Mills energy functional, deriving monotonicity formula and vanishing theorem.
result Monotonicity and vanishing theorems for exponential Yang-Mills fields.
The paper defines and studies new types of submanifolds in a unit sphere.
problem Variational problems of curvature tensors for submanifolds.
method Euler-Lagrange equations for Normal-Yang-Mills and Tangent-Yang-Mills submanifolds.
result Infinitely many non-trivial examples of Normal-Yang-Mills and Tangent-Yang-Mills submanifolds are constructed.
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 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…
Explains a 1978 construction for Yang-Mills instantons.
problem None explicitly stated; focuses on explaining a construction.
method Atiyah-Drinfeld-Hitchin-Manin construction
result Explains the ADHM construction of Yang-Mills instantons.
Extends weak continuity of Yang-Mills connections to a broader class.
problem Weak compactness of Ω-Yang-Mills connections. method Compensation compactness argument applied to Yang-Mills fields.
result Weak continuity result extended to Ω-Yang-Mills connections. Study resolves conjectures on hypercritical deformed Hermitian-Yang-Mills equation.
problem Resolving conjectures on hypercritical deformed Hermitian-Yang-Mills equation.
method Study compact Kähler manifolds and resolves conjectures of Collins-Yau.
result Resolves two conjectures of Collins-Yau.
Study on Yang-Mills equations on conformally compact manifolds, finding obstructions and asymptotics.
problem Obstructing higher conformal Yang-Mills equations on conformally compact manifolds.
method Formal asymptotics, Dirichlet-to-Neumann maps, higher transverse derivative boundary operators.
result Obstructing current is the variation of a conformally invariant coefficient in the interior Yang-Mills energy expansion.
Study the deformation theory of Einstein-Yang-Mills system on compact manifolds.
problem Deformation theory of Einstein-Yang-Mills system on compact manifolds.
method Slice theorem, linearization analysis, essential deformation characterization.
result Realize moduli space of Einstein-Yang-Mills pairs as an analytic set in a finite-dimensional tame Fréchet manifold.
Flat Yang-Mills connections on pinched manifolds.
problem Stability of Yang-Mills connections on compact manifolds.
method Pinching conditions and weak stability criteria.
result No non-flat weakly stable Yang-Mills connections on δ(n)-pinched compact simply-connected Riemannian manifolds.
Study proves uniqueness of Yang-Mills field tangent cones in arbitrary dimensions.
problem Proving uniqueness of Yang-Mills field tangent cones.
method Log-epiperimetric inequality, Luckhaus type lemma, and curvature concentration exclusion.
result Uniqueness of tangent cones for Yang-Mills fields in arbitrary dimensions.
Study Yang-Mills connections on conformally compact manifolds, proving existence of extensions.
problem Existence of Yang-Mills connections on conformally compact manifolds.
method Proving existence of Yang-Mills connections for small deformations.
result Confirming the existence of Yang-Mills connections in the interior of the manifold.
The paper constructs examples of coupled Dirac-Yang-Mills pairs on Riemannian manifolds.
problem Constructing coupled Dirac-Yang-Mills pairs on Riemannian manifolds.
method Constructing spherically symmetric Dirac-Yang-Mills pairs on Riemannian 3-manifolds with SU(2) structure group.
result The construction yields coupled solutions, including on S^1(r_1) x S^2(r_2) for certain radii.
Study on a deformed Hermitian-Yang-Mills equation on compact Kähler manifolds.
problem Existence of solutions to the hypercritical deformed Hermitian-Yang-Mills equation.
method Introduce coerciveness and properness of the J-functional on almost calibrated (1,1)-forms.
result Equivalence of coerciveness and properness to the existence of solutions.
Paper proves no stable Yang-Mills fields on spheres.
problem Existence of stable Yang-Mills fields on spheres.
method Analyzes C2 neighborhoods of Euclidean sphere metrics and warped product manifolds. result No nontrivial weakly stable Yang-Mills connections in specified neighborhoods.
Study on hermitian Yang-Mills connections on blown-up manifolds.
problem Analyzing hermitian Yang-Mills connections on blown-up Kähler manifolds.
method Investigates connections for pullback vector bundles under specific conditions.
result Provides numerical criterion for convergence of hermitian Yang-Mills connections.
A local monotonicity formula for the Yang-Mills-Higgs flow on G-bundles over Rn (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.
problem Yang-Mills theory with specific curvature constraints.
method Proof of existence for non-degenerate traceless Ricci curvature.
result Locally exists SO(3) Yang-Mills field matching curvature. The paper studies decay near singularities of 3d Yang-Mills-Higgs fields.
problem Understanding isolated singularities of 3d Yang-Mills-Higgs fields.
method Derives decay estimates and applies removable singularity theorems.
result Generalizes removable singularity theorems for 3d Yang-Mills-Higgs fields.
The paper finds asymmetric Type-I blowup solutions for Yang-Mills flow.
problem Existence of asymmetric Type-I blowup solutions for Yang-Mills flow.
method Constructing an infinite-dimensional family of solutions for the Yang-Mills flow on RnimesSO(n) for 5≤n≤9. result Existence of asymmetric Type-I blowup solutions for the Yang-Mills flow.
Stable solutions to Yang-Mills-Higgs equations on spheres and tori identified.
problem Stable solutions to abelian Yang-Mills-Higgs equations on S2 and T2. method Reduction to vortex equations and application of Bourguignon-Lawson's method for stable SU(2) Yang-Mills connections. result Stable solutions to abelian Yang-Mills-Higgs equations on S2 and T2 are identified as satisfying vortex equations. 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.
problem Yang-Mills functional over circle bundles with two-forms.
method Dimensional reduction and Euler-Lagrange equations.
result Special three-dimensional solutions satisfy a duality condition.
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.
problem Existence of solutions for deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds.
method Derive a priori estimates under the existence of an admissible C-subsolution; prove existence of solutions under the condition of existence of a supersolution. result Proves existence of solutions for the deformed Hermitian-Yang-Mills equation.
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…
The paper proves parabolic gap theorems for Yang-Mills energy.
problem Yang-Mills energy and instantons on various manifolds.
method Parabolic Yang-Mills flow and Morrey norms.
result Spaces of connections with Yang-Mills energy less than a certain threshold deformation-retract onto spaces of instantons.
Study on Yang-Mills fields on S4 proving self-duality constraints.
problem Proving self-duality of weakly stable Yang-Mills fields on S4. method Investigating irreducible connections under self-duality assumption.
result Irreducible Yang-Mills fields on S4 are either self-dual or anti-self-dual. The study refines stability results for Yang-Mills fields and harmonic maps.
problem Stability of Yang-Mills fields and harmonic maps.
method Refinement of stability results using Jacobi operator over S^m.
result Refined stability results and Morse index estimates.
Proves local existence and extension principle for Einstein Yang--Mills system with spherical symmetry.
problem Local existence and stability of the spherically symmetric Einstein Yang--Mills system.
method Employed an L2-based method to prove local existence and establish an extension principle. result Established local existence and extension principle for the SSEYM with H1 data. Sharp convergence theorem for Yang-Mills flow on ALE manifolds proved.
problem Proving convergence of Yang-Mills flow on ALE gravitational instantons.
method Noncompact version of the 'parabolic gap theorem'.
result Sharp convergence theorem for Yang-Mills flow on ALE 4-manifolds.
Study on existence of harmonic metrics for non-Hermitian Yang-Mills bundles.
problem Existence of harmonic metrics in non-Hermitian Yang-Mills bundles.
method Examined compact Kähler manifolds and equivalence to semisimplicity of NHYM bundles.
result Existence of harmonic metrics is equivalent to semisimplicity of NHYM bundles.
The paper studies gauge fields on coherent sheaves and their Yang-Mills properties.
problem Analyzing gauge fields on coherent sheaves and their Yang-Mills properties.
method Defined necessary and sufficient conditions for Yang-Mills fields, introduced cohomology classes, and analyzed holomorphic and meromorphic gauge fields.
result Existence of curves of Yang-Mills fields connecting vacuum states on bundles over the torus T2. Let F:[0,∞)→[0,∞) be a strictly increasing C2 function with F(0)=0. We unify the concepts of F-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce F-Yang-Mills fields, F-degree, F-lower degree, and generalized Yang-Mills-Born-Infeld…
Stability of Morse index for Yang-Mills connections in 4D.
problem Stability of critical points in Yang-Mills energy relaxation.
method Establishing lower semi-continuity of Morse index and upper continuity of Morse index plus nullity.
result Yang-Mills fields are more stable than harmonic maps in 4D.
Stability of Yang-Mills connections' Morse indices and nullity in 4D.
problem Stability of Yang-Mills connections' Morse indices and nullity in 4D under weak convergence.
method Proves stability results of the Morse index plus nullity of Yang-Mills connections in dimension 4 under weak convergence.
result Stability of the sum of Morse indices and nullity of a sequence of Yang-Mills connections.
In this paper, we introduce an α-flow for the Yang-Mills functional in vector bundles over four dimensional Riemannian manifolds, and establish global existence of a unique smooth solution to the α-flow with smooth initial value. We prove that the limit of solutions of the α-flow as α\to 1 is a weak solution to the Yan…
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…