Jiayu Li

Semi-stable Higgs sheaves and Bogomolov type inequality

In this paper, we study semi-stable Higgs sheaves over compact Kähler manifolds. We prove that there is an admissible approximate Hermitian-Einstein structure on a semi-stable reflexive Higgs sheaf and consequently, the Bogomolov type inequality holds on a semi-stable reflexive Higgs sheaf.

The Symplectic Critical Surfaces in a Kähler Surface

In this paper, we study the functional \(L_\beta =\int _\varSigma \frac{1}{\cos ^\beta \alpha }d\mu ,~\beta \ne -1\) in the class of symplectic surfaces. We derive the Euler-Lagrange equation. We call such a critical surface a \(\beta \)-symplectic critical surface. When \(\beta =0\), it is the equation of minimal surfaces. When \(\beta \ne 0\), a minimal surface with constant Kahler angle satisfies this equation, especially, a holomorphic curve or a special Lagrangian surface satisfies this equation. We study the properties of the \(\beta \)-symplectic critical surfaces.