Talk page
Title:
Extremal Metrics on Toric Manifolds and Affine Techniques
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Abstract:
In a sequence of papers, Donaldson initiated a program to study the extremal metrics on toric manifolds and solved the problem for cscK metrics on toric surfaces. For toric manifolds, the equation of extremal metrics can be reduced to a real 4th-order partial differential equation on the Delzant polytope, called the Abreu equation, which is similar to the maximal equation in affine geometry. The affine techniques play important role. In joint papers with Bohui Chen and Li Sheng we apply the affine techniques to extend the existence result in dimension 2 to extremal metrics. In this talk we explain our main idea and methods.
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