Calabi's conjecture and some new results in algebraic geometry.
We announce a proof of Calabi's conjectures on the Ricci curvature of a compact Kähler manifold and then apply it to prove some new results in algebraic geometry and differential geometry. For example, we prove that the only Kähler structure on a complex projective space is the standard one.
Yau
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Mathematics Department, Stanford University, Stanford, California 94305.