Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds

Abstract: The Yau-Tian-Donaldson conjecture concerns the equivalence between existence of Kähler metrics with constant scalar curvature on a polarized complex manifold, and an algebro-geometric K-stability condition. It has been solved in the case of anticanonically polarized manifolds by Chen-Donaldson-Sun, and in the case of toric surfaces by Donaldson. In both cases, a condition weaker than the expected K-stability suffices, and in the toric case, Donaldson translates the K-stability into a convex polytope geometry problem. In this talk, I will present progress on the Yau-Tian-Donaldson conjecture for spherical varieties, and in particular, a resolution of this conjecture in the case of polarized manifolds of cohomogeneity one.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

( paper | video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Riemannian geometry.

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