arXiv research

Survey on complex submanifolds in Euclidean spaces.

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

Paper solves a complex equation for smooth domains.

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

Developed a new symmetric hyperbolic formulation for Einstein-Yang-Mills system.

Study on Yang-Mills fields on $S^4$ proving self-duality constraints.

We show a sharp conformally invariant gap theorem for Yang-Mills connections in dimension 4 by exploiting an associated Yamabe-type problem.

In this paper we complete the proof of the existence of multiple solutions (and, in particular, non minimal ones), to the epsilon-Dirichlet problem obtained as a variational problem for the SU(2)-epsilon-Yang Mills functional. This is equivalent to proving the existence of multiple solutions to the Dirichlet problem fo…

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

Stability of Morse index for Yang-Mills connections in 4D.

Du, Kakade, Wang, and Yang recently established intriguing lower bounds on sample complexity, which suggest that reinforcement learning with a misspecified representation is intractable. Another line of work, which centers around a statistic called the eluder dimension, establishes tractability of problems similar to t…

In this note, we consider the problem of constructing knot invariants from Yang-Baxter operators associated to (unitary associative) algebra structures. We first compute the enhancements of these operators. Then, we conclude that Turaev's procedure to construct knot invariants, as modified by Murakami, invariably produ…

Paper solves tensor problem for holomorphic vector bundles.

Study wormholes in Einstein-Yang-Mills theory with a phantom field.

Paper proves conditions for rational homology complex projective planes with singularities.

The paper constructs new algebraic structures from Lie algebras and ternary Nambu-Lie algebras, leading to Yang-Baxter operators.

Solved a conjecture about rational homology projective planes with quotient singularities.

We review the notions of (weak) Hermitian-Yang-Mills structure and approximate Hermitian-Yang-Mills structure for Higgs bundles. Then, we construct the Donaldson functional for Higgs bundles over compact Kähler manifolds and we present some basic properties of it. In particular, we show that its gradient flow can be wr…

Every rack $Q$ provides a set-theoretic solution $c_Q$ of the Yang-Baxter equation. This article examines the deformation theory of $c_Q$ within the space of Yang-Baxter operators over a ring $\A$, a problem initiated by Freyd and Yetter in 1989. As our main result we classify deformations in the modular case, which ha…

Montgomery-Yang problem predicts that every pseudofree differentiable circle action on the 5-dimensional sphere has at most 3 non-free orbits. Using a certain one-to-one correspondence, Kollár formulated the algebraic version of the Montgomery-Yang problem: every projective surface $S$ with the second Betti number $b_2…

Let $F: [0, \infty) \to [0, \infty)$ be a strictly increasing $C^2$ 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…

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,…

Stability of Minkowski space-time in Einstein-Yang-Mills system proven.

The paper solves a problem related to Higgs bundles and Hermitian metrics.

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

Stability of Minkowski space-time in higher dimensions proven for arbitrary small perturbations.

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

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

We review the notions of (weak) Hermitian-Yang-Mills structure and approximate Hermitian-Yang-Mills structure for Higgs bundles. Then, we construct the Donaldson functional for Higgs bundles over compact Kähler manifolds and we present some basic properties of it. In particular, we show that its gradient flow can be wr…

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…

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

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

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…

Starting from the free field realization of Kac-Moody Lie algebra, we define a generalized Yang-Yang function. Then for the Lie algebra of type $A_{n}$, we derive braiding and fusion matrix by braiding the thimble from the generalized Yang-Yang function. One can construct a knots invariant $H(K)$ from the braiding and …

Compact formulas for Yang-Mills conditions on conformal manifolds.

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

Adjusts Yang-Baxter operators for HOMFLYPT polynomials.

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…

Montgomery-Yang problem predicts that every pseudofree differentiable circle action on the 5-dimensional sphere ${\mathbb S}^5$ has at most 3 non-free orbits. Using a certain one-to-one correspondence, Kollár formulated the algebraic version of the Montgomery-Yang problem: every projective surface $S$ with quotient sin…

The paper classifies extensions of Yang-Mills-type theories, proving maximality and universality are dense properties.

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.

Flat Yang-Mills connections on pinched manifolds.