The collapsing rate of the Kähler–Ricci flow with regular infinite time singularity

By Frederick Tsz-Ho Fong, Zhou Zhang. 2012

55 citations recorded by the source corpus.

We study the collapsing behavior of the Kaehler-Ricci flow on a compact Kaehler manifold X admitting a holomorphic submersion X -> S coming from its canonical class, where S is a Kaehler manifold with dim S < dim X. We show that the flow metric degenerates at exactly the rate of e^{-t} as predicted by the cohomology information, and so the fibers collapse at the optimal rate diameter ~ e^{-t/2}. Consequently, it leads to some analytic and geometric extensions to the regular case of Song-Tian's works on elliptic and Calabi-Yau fibrations. Its applicability to general Calabi-Yau fibrations with possibly singular fibers will also be discussed in local sense.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2f26019cfbcb8637aadd6240fc42a7df3c88c818

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Infinite time singularities of the Kähler-Ricci flow (2014, methodology): “The second setup is as follows (see Song and Tian [20; 22; 21], Fong and Zhang [5] and Tosatti, Weinkove and Yang [27]).”