Luen Fai Tam, CUHK, Hong Kong

Nonnegatively curved Kähler manifolds with quadratic curvature decay

We will report some recent joint works with Albert Chau on the complex structure of a noncompact complete Kähler manifold M with nonnegative holomorphic bisectional curvature. We will discuss the proof of the following result: If M has maximal volume growth, then M is biholomorphic to Cⁿ. Note that by a result of Ni, such a manifold must have quadratic curvature decay. The proof will use this fact in an essential way.