arXiv research

Introduce a flow for prescribed Hermitian-Yang-Mills tensors

Construct Hermitian-Einstein metrics on stable holomorphic vector bundles using dynamical methods.

Paper solves tensor problem for holomorphic vector bundles.

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

The flow proves a theorem for Fano manifolds.

For any locally defined $G_{2}-$structure and Hermitian-Yang-Mills connection on $S^{6}$, the $G_{2}-$monopole equation always admits a local solution that is asymptotic to the HYM-connection.

We consider the Toda systems of VHS type with singular sources and provide a criterion for the existence of solutions with prescribed asymptotic behaviour near singularities. We also prove the uniqueness of solution. Our approach uses Simpson's theory of constructing Higgs-Hermitian-Yang-Mills metrics from stability.

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

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

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

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

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

Paper solves a complex equation for smooth domains.

Characterizes tangent cones for specific connections on reflexive sheaves.

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

Study disproves conjecture about Hermitian-Yang-Mills solutions.

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…

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

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

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.

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

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

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

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

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…

Develops harmonic metrics for Hull-Strominger system stability.

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

Paper proves solvability condition for complex equation on special submanifolds.

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

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…

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…

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

We construct local examples of singular Hermitian Yang-Mills connections over $B_1\subset \mathbb{C}^3$ with uniformly bounded $L^2$-energy, but the number of essential singular points can be arbitrarily large.

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

Solves supercritical dHYM on projective manifolds with specific conditions.

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 first study the degeneration of a sequence of Hermitian-Yang-Mills metrics with respect to a sequence of balanced metrics on a Calabi-Yau threefold $\hat{X}$ that degenerates to the balanced metric constructed by Fu, Li, and Yau on the complement of finitely many (-1,-1)-curves in $\hat{X}$. Then under some assumpti…

Paper proves Hermitian-Yang-Mills metrics for stable Kähler bundles.

Study on a nonlinear elliptic equation on compact Hermitian manifolds.

In this paper, we analyze the asymptotic behaviour of the Hermitian-Yang-Mills flow over a compact non-Kähler manifold $(X,g)$ with the Hermitian metric $g$ satisfying the Gauduchon and Astheno-Kähler condition.

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.

Proves existence and uniqueness of weak solutions for specific equations.

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

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.

The note proves a metric equivalence for stable bundles on surfaces.

In this paper, we study the deformed Hermitian-Yang-Mills equation on compact Kähler manifold with non-negative orthogonal bisectional curvature. We prove that the curvatures of deformed Hermitian-Yang-Mills metrics are parallel with respect to the background metric if there exists a positive constant $C$ such that $-\…

In this paper, we study the asymptotic behavior of the Hermitian-Yang-Mills flow on a reflexive sheaf. We prove that the limiting reflexive sheaf is isomorphic to the double dual of the graded sheaf associated to the Harder-Narasimhan-Seshadri filtration, this answers a question by Bando and Siu.