Bergman kernels and eigenvalue estimate of $\bar{\partial }$-laplacian

Zhiwei Wang

Let $(X,\omega )$ be a compact Kähler manifold. Let $(L,h)$ be a hermitian holomorphic line bundle over $X$, such that ${\Theta }_{L,h}\ge -\epsilon \omega$ for a small $\epsilon >0$, $E$ be a h…