Related papers: Hermitian-Yang-Mills connections on some complete …

We investigate quantization properties of Hermitian metrics on holomorphic vector bundles over homogeneous compact K\"ahler manifolds. This allows us to study operators on Hilbert function spaces using vector bundles in a new way. We show…

In this paper, we study the non-Hermitian Yang-Mills (NHYM for short) bundles over compact K\"ahler manifolds. We show that the existence of harmonic metrics is equivalent to the semisimplicity of NHYM bundles, which confirms the Conjecture…

We prove an analogue of the Donaldson-Uhlenbeck-Yau theorem for asymptotically cylindrical K\"ahler manifolds: If $\mathscr{E}$ is a reflexive sheaf over an ACyl K\"ahler manifold, which is asymptotic to a $\mu$-stable holomorphic vector…

In this paper, we solve the prescribed Hermitian-Yang-Mills tensor problem. Let $ E $ be a holomorphic vector bundle over a compact K\"ahler manifold $(M,\omega_g) $. Suppose that there exists a smooth Hermitian metric $ h_0 $ on $E$ such…

In this short note, we show that, assuming a conjecture of Arcara and Miles, a line bundle on a smooth complex projective surface admits a deformed Hermitian-Yang-Mills metric if and only if it is stable in the ``large scaling limit" with…

We consider a sufficiently smooth semi-stable holomorphic vector bundle over a compact K\"ahler manifold. Assuming the automorphism group of its graded object to be abelian, we provide a semialgebraic decomposition of a neighbourhood of the…

For a holomorphic vector bundle over a compact K\"ahler orbifold, the slope stability of the bundle is shown to be equivalent to the existence of a Hermitian-Einstein metric or to the properness of a certain functional introduced by…

This paper begins to study the limiting behavior of a family of Hermitian Yang-Mills (HYM for brevity) metrics on a class of rank two slope stable vector bundles over a product of two elliptic curves with K\"ahler metrics $\omega_\epsilon$…

The deformed Hermitian-Yang-Mills equation is a complex Hessian equation on compact K\"ahler manifolds that corresponds to the special Lagrangian equation in the context of the Strominger-Yau-Zaslow mirror symmetry. Recently, Chen proved…

We prove that the existence of a $Z$-positive and $Z$-critical Hermitian metric on a rank 2 holomorphic vector bundle over a compact K\"ahler surface implies that the bundle is $Z$-stable. As particular cases, we obtain stability results…

We study Yang-Mills connections on holomorphic bundles over complex K\"ahler 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…

In this paper, we show that if a holomorphic vector bundle is slope polystable with respect to a K\"{a}hler class, then it admits a Hermitian-Yang-Mills metric with respect to a suitable K\"{a}hler current with singularities in higher…

Let $X$ be a compact complex manifold of dimension $n$ and let $m$ be a positive integer with $m\leq n$. Assume that $X$ admits a K\"ahler metric $\omega$ and a weakly positive, $\partial\bar\partial$-closed, smooth $(n-m,\,n-m)$-form…

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…

We adapt the notions of stability of holomorphic vector bundles in the sense of Mumford-Takemoto and Hermitian-Einstein metrics in holomorphic vector bundles for canonically polarized framed manifolds, i.e. compact complex manifolds X…

We study the twisted ampleness criterion due to Collins, Jacob and Yau on surfaces, which is equivalent to the existence of solutions to the deformed Hermitian-Yang-Mills (dHYM) equation. When $X$ is a Weierstrass elliptic K3 surface, and…

We introduce the $J$-equation on holomorphic vector bundles over compact K\"ahler manifolds and investigate some fundamental properties as well as examples of solutions. In particular, we provide an algebraic condition called (asymptotic)…

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

This short note includes three results: $(1)$ If a reflexive sheaf $\mathcal{E}$ on a log terminal K\"{a}hler-Einstein variety $(X,\omega)$ is slope stable with respect to a singular K\"{a}hler-Einstein metric $\omega$, then $\mathcal{E}$…

In this paper, we extend a result of Gao Chen regarding the solvability of the twisted deformed Hermitian Yang-Mills equations on compact K\"ahler manifolds to allow for the twisting function to be non-constant and slightly negative in all…