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Ye-Kai Wang

2009-06-18
09:30:00 - 12:00:00

Calabi-Yau Theorem

110 , Old Mathematics Building

The Calabi-Yau theorem says for any (1,1)-form T = iT¯kjdzj ^ d¯zk on a compact K¨ahler manifold (M, !) with T 2 c1(M), we can find another K¨ahler metric with [˜!]=[!] such that Ric(˜!) = T. We would prove this theorem following Prof. Phong’s lecture note. The prerequisite includes basic properties of curvature tensor on K¨ahler manifold, @ ¯@−lemma, and the Schauder estimates for elliptic operators.