The conical Kähler-Ricci flow with weak initial data on Fano manifold

Abstract

In this paper, we prove the long-time existence and uniqueness of the conical Kähler-Ricci flow with weak initial data which admits $L^p$ density for some $p>1$ on Fano manifold. Furthermore, we study the convergence behavior of this kind of flow.

30 pages

References in corpus (8)

• A Brunn-Minkowski type inequality for Fano manifolds and the Bando-Mabuchi uniqueness theorem
• The Kahler-Ricci flow through singularities
• Smooth approximations of the Conical Kahler-Ricci flows
• The conical Kähler-Ricci flow on Fano manifolds
• On the long time behaviour of the Conical Kähler- Ricci flows
• $C^{2,\alpha }$-estimate for conical Kähler-Ricci flow
• Properness of log $F$-functionals
• Isoperimetric inequality along the twisted Kähler-Ricci flow

Cited by in corpus (2)

• Smooth approximations of the Conical Kahler-Ricci flows
• Metric contraction of the cone divisor by the conical Kähler-Ricci flow