On the Kahler Ricci flow on projective manifolds of general type
By Bin Guo. 2015
50 citations recorded by the source corpus.
We consider the K\"ahler Ricci flow on a smooth minimal model of general type, we show that if the Ricci curvature is uniformly bounded below along the K\"ahler-Ricci flow, then the diameter is uniformly bounded. As a corollary we show that under the Ricci curvature lower bound assumption, the Gromov-Hausdorff limit of the flow is homeomorphic to the canonical model. Moreover, we can give a purely analytic proof of a recent result of Tosatti-Zhang (\cite{TZ}) that if the canonical line bundle $K_X$ is big and nef, but not ample, then the flow is of Type IIb.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/ddbba0defdfd6a32f88166c35372a9ddae599efd
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
- G'abor Sz'ekelyhidi
- Gang Liu
- Chi Li
- Abdellah Lahdili
- Jian Song
- Duong H. Phong
- Mattias Jonsson
- S. Boucksom
In Geometry and Topology
- G'abor Sz'ekelyhidi
- Gang Liu
- Chi Li
- Abdellah Lahdili
- Jian Song
- Duong H. Phong
- Mattias Jonsson
- Tam'as Darvas
Citations in the corpus
- Gromov–Hausdorff limits of Kähler manifolds with Ricci curvature bounded below (2018, methodology): “It follows from Tian-Zhang [47], that if K is large (not necessarily bounded a priori), then we have a well defined Kähler-Ricci flow solution ηt for t ∈ [0, 1].”