Weak solutions to degenerate complex Monge–Ampère flows II

• Published in: Advances in mathematics (New York. 1965) Vol. 293; pp. 37 - 80
• Main Authors: Eyssidieux, Philippe, Guedj, Vincent, Zeriahi, Ahmed
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 30.04.2016; Elsevier
• Subjects: Canonical singularities; Complex Monge–Ampère flows; Complex Variables; Differential Geometry; Kähler–Ricci flow; Mathematics; Viscosity solutions; Kähler–Ricci flow; Canonical singularities; Complex Monge–Ampère flows; Viscosity solutions
• ISSN: 0001-8708; 1090-2082; 1090-2082
• DOI: 10.1016/j.aim.2016.02.010

Studying the (long-term) behavior of the Kähler–Ricci flow on mildly singular varieties, one is naturally led to study weak solutions of degenerate parabolic complex Monge–Ampère equations. The purpose of this article, the second of a series on this subject, is to develop a viscosity theory for degenerate complex Monge–Ampère flows on compact Kähler manifolds. Our general theory allows in particular to define and study the (normalized) Kähler–Ricci flow on varieties with canonical singularities, generalizing results of Song and Tian.