Degenerate complex Monge-Ampère flows on strictly pseudoconvex domains

Abstract

We study the equation $\dot{u}=\log \det (u_{\alpha \bar{\beta }})+f(t,z,u)$ in domains of ${\mathbb{C}}^n$. This equation has a close connection with the Kähler-Ricci flow. In this paper, we consider the case of the boundary conditions are smooth and the initial conditions are bounded.

In this version, we fix a mistake in the condition of Theorem 0.1 (replace "φ(z,t)=u_0(z)" by "φ(z,0)=u_0(z)"). We also define δ_m in the page 29 and correct a mistake in the page 30

References in corpus (3)

• The Kähler-Ricci flow on surfaces of positive Kodaira dimension
• Kahler-Ricci flow on stable Fano manifolds
• Regularity of weak solutions of a complex Monge-Ampère equation