Nonexistence for complete Kähler Einstein metrics on some noncompact manifolds

Peng Gao, Shing-Tung Yau, Wubin Zhou

Let $M$ be a compact Kähler manifold and $N$ be a subvariety with codimension greater than or equal to 2. We show that there are no complete Kähler--Einstein metrics on $M-N$. As a…