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arXiv · 1905.01276

Convergence of the weak K\"ahler-Ricci Flow on manifolds of general type

Tat Dat Tô
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Abstract

We study the K\"ahler-Ricci flow on compact K\"ahler manifolds whose canonical bundle is big. We show that the normalized K\"ahler-Ricci flow has long time existence in the viscosity sense, is continuous in a Zariski open set, and converges to the unique singular K\"ahler-Einstein metric in the canonical class. The key ingredient is a viscosity theory for degenerate complex Monge-Amp\`ere flows in big classes that we develop, extending and refining the approach of Eyssidieux-Guedj-Zeriahi.

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Tat Dat Tô. 2019-05-03. Convergence of the weak K\"ahler-Ricci Flow on manifolds of general type. https://doi.org/10.1093/imrn%2Frnz256

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