Convergence of the weak Kähler-Ricci Flow on manifolds of general type

Abstract

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

details added in proof of Theorem 4.3

References in corpus (2)

• KAWA lecture notes on the Kähler-Ricci flow
• A viscosity approach to the Dirichlet problem for degenerate complex Hessian type equations