Symmetric differentials and jets extension of $L^2$ holomorphic functions II: Explicit form

Abstract

For a symmetric differential on the compact quotient $\Sigma ={\mathbb{B}}^n/\Gamma$ of the complex unit ball ${\mathbb{B}}^n\subset {\mathbb{C}}^n$ by a discrete subgroup $\Gamma \subset \mathrm{Aut}({\mathbb{B}}^n)$, there exists a corresponding weighted $L^2$-holomorphic function on $({\mathbb{B}}^n\times {\mathbb{B}}^n)/\Gamma$, where $\Gamma$ acts diagonally on ${\mathbb{B}}^n\times {\mathbb{B}}^n$. In this paper, we give an explicit description of this correspondence and derive several applications based on its explicit form.

20 pages, any comments welcome