Faculty Research Perspectives

The uniformization theorem and its generalization

Jian Song

April 21, 3:30 PM in Hill 705



Abstract.

The uniformization theorem for surfaces says any Riemann surface admits a Riemannian metric of constant scalar curvature. Yau's solution to the Calabi conjecture predicts the existence of Einstein Kahler metrics on any Kahler manifolds of negative or vanishing first Chern class. However, the uniformization theorem does not hold for higher dimension in general. In this talk, we discuss the program of finding canonical metrics on Kahler manifolds in relation to partial differential equations and algebraic geometry.

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