Current browse context:
math.DG
Change to browse by:
References & Citations
Mathematics > Differential Geometry
Title: Collapsing immortal Kähler-Ricci flows
(Submitted on 7 May 2024)
Abstract: We consider the K\"ahler-Ricci flow on compact K\"ahler manifolds with semiample canonical bundle and intermediate Kodaira dimension, and show that the flow collapses to a canonical metric on the base of the Iitaka fibration in the locally smooth topology and with bounded Ricci curvature away from the singular fibers. This follows from an asymptotic expansion for the evolving metrics, in the spirit of recent work of the first and third-named authors on collapsing Calabi-Yau metrics, and proves two conjectures of Song and Tian.
Link back to: arXiv, form interface, contact.