Abstract

We will first recall the stability of vector bundles and Donaldson-Uhlenbeck-Yau theorem. Then we will talk about Bando-Siu’s generalization of the DUY theorem to reflexive sheaves, i.e. the existence of canonical metrics on reflexive sheaves. Finally we prove the Bando-Siu conjecture which are joint work with Xi Zhang and Chuanjing Zhang.