arXiv research

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

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

Characterizes tangent cones for specific connections on reflexive sheaves.

Local examples of singular connections with bounded energy.

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

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

Construct a Hermitian metric on non-Hermitian Yang--Mills moduli spaces near the Hermitian locus.

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…

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

Consider a vector bundle over a Kähler manifold which admits a Hermitian Yang-Mills connection. We show that the pullback bundle on the blowup of the Kähler manifold at a collection of points also admits a Hermitian Yang-Mills connection, for Kähler classes on the blowup which make the exceptional divisors small. Our p…

We give a simple direct proof of uniqueness of tangent cones for singular projectively Hermitian Yang-Mills connections on reflexive sheaves at isolated singularities modelled on $μ$-polystable holomorphic bundles over $\mathbf{P}^{n-1}$.

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…

Study on a nonlinear elliptic equation on compact Hermitian manifolds.

We give an example of a homogeneous reflexive sheaf over $\mathbb{C}^3$ which admits a non-conical Hermitian Yang-Mills connection. This is expected to model bubbling phenomenon along complex codimension 2 submanifolds when the Fueter section takes zero value.

We generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle on a compact Kaehler manifold, with structure group a connected linear algebraic reductive group, is se…

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

In this paper we study the analytic tangent cones of admissible Hermitian-Yang-Mills connections near a homogeneous singularity of a reflexive sheaf, and relate it to the Harder-Narasimhan-Seshadri filtration. We also give an algebro-geometric characterization of the bubbling set. This strengthens our previous result.

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

New criterion found for Hermitian-Yang-Mills metrics on non-compact Kähler manifolds.

We introduce $Z$-critical connections for holomorphic vector bundles and prove their existence under stability conditions.

A recent paper (arxiv.org:1810.00025) studied properties of a compactification of the moduli space of irreducible Hermitian-Yang-Mills connections on a hermitian bundle over a projective algebraic manifold. In this follow-up note, we show that the Yang-Mills flow at infinity on the space of semistable integrable connec…

The paper studies deformations of Hermitian Yang-Mills and Donaldson-Thomas connections on $G_2$-manifolds.

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 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…

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 proves a theorem and characterizes connections over normal varieties.

Study of deformed Hermitian Yang-Mills equations with variable Kähler metrics.

We study and construct non-abelian hermitian Yang-Mills (HYM) instantons on Calabi-Yau cones. By means of a particular isometry preserving ansatz, the HYM equations are reduced to a novel Higgs-Yang-Mills flow on the Einstein-Kahler base. For any 2d-dimensional Calabi-Yau cone, we find explicit solutions of the flow eq…

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

The paper studies HYM connections on stable vector bundles over Kähler manifolds.

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

Let $X$ be a compact connected Kähler--Einstein manifold with $c_1(TX)\, \geq\, 0$. If there is a semistable Higgs vector bundle $(E\,,θ)$ on $X$ with $θ\,\not=\,0$, then we show that $c_1(TX)=0$, any $X$ satisfying this condition is called a Calabi--Yau manifold, and it admits a Ricci--flat Kähler form \cite{Ya}. Let …

Study on $G_{2}$-instantons and Hermitian Yang-Mills connections, focusing on spectrum analysis.

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

The paper finds explicit instantons on a specific 6-manifold.

In this monograph, we develop results on global existence and convergence of solutions to abstract gradient flows on Banach spaces for a potential function that obeys the Lojasiewicz-Simon gradient inequality. We prove a Lojasiewicz-Simon gradient inequality for the Yang-Mills energy functional over closed, smooth Riem…

Study the long-time behavior of Hermitian-Yang-Mills flow on non-Kähler manifolds.

Introduce a flow for prescribed Hermitian-Yang-Mills tensors

Paper solves tensor problem for holomorphic vector bundles.

Let $X\rightarrow {\mathbb P}^1$ be an elliptically fibered $K3$ surface, admitting a sequence $ω_{i}$ of Ricci-flat metrics collapsing the fibers. Let $V$ be a holomorphic $SU(n)$ bundle over $X$, stable with respect to $ω_i$. Given the corresponding sequence $Ξ_i$ of Hermitian-Yang-Mills connections on $V$, we prove …

The paper confirms the solvability of a complex equation for a 4D manifold.

Paper solves a complex equation for smooth domains.

Study disproves conjecture about Hermitian-Yang-Mills solutions.

Study on existence of harmonic metrics for non-Hermitian Yang-Mills bundles.

New equation approximates Kähler potentials using Hermitian-Yang-Mills metrics.

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

The paper examines inequalities for Chern numbers on specific 4D Kähler manifolds.

From string theory, the notion of deformed Hermitian Yang-Mills connections has been introduced by Mariño, Minasian, Moore and Strominger. After that, Leung, Yau and Zaslow proved that it naturally appears as mirror objects of special Lagrangian submanifolds via Fourier-Mukai transform between dual torus fibrations. In…