arXiv research

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

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

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

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

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

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

Paper solves a complex equation for smooth domains.

Introduces new equations linking Kähler-Einstein and Hermitian-Yang-Mills theories.

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

Study deformed Hermitian-Yang-Mills equation on complex projective space blowup.

Surveying progress on deformed Hermitian-Yang-Mills equation and its connections to stability.

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 …

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

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 …

Stable blowup solutions found for supercritical Yang-Mills equations.

The paper proves conditions for solutions of $J$-equation and deformed Hermitian-Yang-Mills equation on holomorphic submersions.

Paper proves solvability condition for complex equation on special submanifolds.

The purpose of this paper is to introduce the Ricci Yang-Mills soliton equations on nilpotent Lie groups. In the 2-step nilpotent setting, we show that these equations are strictly weaker than the Ricci soliton equations. Using techniques from Geometric Invariant Theory, we develop a procedure to build many different k…

Study disproves conjecture about Hermitian-Yang-Mills solutions.

Integrability of the (2+1)-dimensional Gauss-Codazzi-Mainardi equation is considered. It is shown that this equation is the particular cases of the Yang-Mills-Higgs-Bogomolny and self-dual Yang-Mills equations.

Some aspects of the multidimensional soliton geometry are considered. The relation between soliton equations in 2+1 dimensions and the Self-Dual Yang-Mills and Bogomolny equations are discussed.

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 Appl. 11 (2012), 185-198, arXiv:1401.7366], when Riemannian manifold $X$ of dim…

Study on a nonlinear elliptic equation on compact Hermitian manifolds.

Solves Dirac equation coupled to vector bundles.

Proves existence and uniqueness of weak solutions for specific equations.

Some aspects of the multidimensional soliton geometry are considered. It is shown that some simples (2+1)-dimensional equations are exact reductions of the Self-Dual Yang-Mills equation or its higher hierarchy.

Proves stability of Minkowski space-time in Einstein-Yang-Mills system.

Study on Yang-Mills equation near instanton-anti-instanton configurations with energy constraints.

Some aspects of the relation between differential geometry of curves and surfaces and multidimensional soliton equations is discussed. The connection between multidimensional soliton equations and Self-dual Yang-Mills equation is studied.

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…

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…

The paper introduces new equations in Kähler geometry and proves their solutions and convexity.

In this paper we introduce a set of equations on a principal bundle over a compact complex manifold coupling a connection on the principal bundle, a section of an associated bundle with Kähler fibre, and a Kähler structure on the base. These equations are a generalization of the Kähler-Yang-Mills equations introduced b…

In this article, we study the analytical properties of the solutions of the complex Yang-Mills equations on a closed Riemannian four-manifold $X$ with a Riemannian metric $g$. The main result is that if $g$ is $good$ and the connection is an approximate ASD connection, then the extra field has a positive lower {bound}.…

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

Study of Yang-Mills fields on 4-manifolds using modified Lévy Laplacians.

Paper establishes estimates for nonlinear equations on compact manifolds.

Proves solvability of general inverse σ_k equations with constant coefficients.

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

On a five dimensional simply connected Sasaki-Einstein manifold, one can construct Yang-Mills theories coupled to matter with at least two supersymmetries. The partition function of these theories localises on the contact instantons, however the contact instanton equations are not elliptic. It turns out that these equa…

Solves supercritical dHYM on projective manifolds with specific conditions.

Proves local existence and extension principle for Einstein Yang--Mills system with spherical symmetry.

The paper proves estimates for vortex-type equations on compact Riemann surfaces.

Study uncoupled solutions to Dirac-Yang-Mills equations on spin manifolds.

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

We study the self-dual Yang-Mills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t'Hooft ansatz is described.

In the context of D-dimensional Euclidean gravity, we define the natural generalisation to D-dimensions of the self-dual Yang-Mills equations, as duality conditions on the curvature 2-form of a Riemannian manifold. Solutions to these self-duality equations are provided by manifolds of SU(2), SU(3), G_2 and Spin(7) holo…

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