Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLimiting Behavior of a Class of Hermitian-Yang-Mills Metrics, I
154
0
0.0
(
0
)
Authors
Jixiang Fu
Ask ChatGPT about the research
No Arabic abstract
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 Kahler metrics $omega_epsilon$ when $epsilonto 0$. Here $omega_epsilon$ are flat and have areas $epsilon$ and $epsilon^{-1}$ on the two elliptic curves respectively. A family of Hermitian metrics on the vector bundle are explicitly constructed and with respect to them, the HYM metrics are normalized. We then compare the family of normalized HYM metrics with the family of constructed Hermitian metrics by doing estimates. We get the higher order estimates as long as the $C^0$-estimate is provided. We also get the estimate of the lower bound of the $C^0$-norm. If the desired estimate of the upper bound of the $C^0$-norm can be obtained, then it would be shown that these two families of metrics are close to arbitrary order in $epsilon$ in any $C^k$ norms.
rate research
Read More
We study a new deformed Hermitian Yang-Mills Flow in the supercritical case. Under the same assumption on the subsolution as Collins-Jacob-Yau cite{cjy2020cjm}, we show the longtime existence and the solution converges to a solution of the deformed Hermitian Yang-Mills equation which was solved by Collins-Jacob-Yau cite{cjy2020cjm} by the continuity method.
We investigate stability of pullback bundles with respect to adiabatic classes on the total space of holomorphic submersions. We show that the pullback of a stable (resp. unstable) bundle remains stable (resp. unstable) for these classes. Assuming the graded object of a Jordan-Holder filtration to be locally free, we obtain a necessary and sufficient criterion for when the pullback of a strictly semistable vector bundle will be stable, in terms of intersection numbers on the base of the fibration. The arguments rely on adiabatic constructions of hermitian Yang-Mills connections together with the classical Donaldson-Uhlenbeck-Yau correspondence.
In this paper, we consider the deformed Hermitian-Yang-Mills equation on closed almost Hermitian manifolds. In the case of hypercritical phase, we derive a priori estimates under the existence of an admissible $mathcal{C}$-subsolution. As an application, we prove the existence of solutions for the deformed Hermitian-Yang-Mills equation under the condition of existence of a supersolution.
We prove an existence result for the deformed Hermitian Yang-Mills equation for the full admissible range of the phase parameter, i.e., $hat{theta} in (frac{pi}{2},frac{3pi}{2})$, on compact complex three-folds conditioned on a necessary subsolution condition. Our proof hinges on a delicate analysis of a new continuity path obtained by rewriting the equation as a generalised Monge-Amp`ere equation with mixed sign coefficients.
We prove a conformally invariant estimate for the index of Schrodinger operators acting on vector bundles over four-manifolds, related to the classical Cwikel-Lieb-Rozenblum estimate. Applied to Yang-Mills connections we obtain a bound for the index in terms of its energy which is conformally invariant, and captures the sharp growth rate. Furthermore we derive an index estimate for Einstein metrics in terms of the topology and the Einstein-Hilbert energy. Lastly we derive conformally invariant estimates for the Betti numbers of an oriented four-manifold with positive scalar curvature.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
