# Bounding Diameter Of Singular Kähler Metric

```@article{Nave2015BoundingDO,
title={Bounding Diameter Of Singular K{\"a}hler Metric},
author={Gabriele La Nave and Gang Tian and Zhenlei Zhang},
journal={American Journal of Mathematics},
year={2015},
volume={139},
pages={1693 - 1731}
}```
• G. L. Nave, Zhenlei Zhang
• Published 11 March 2015
• Mathematics
• American Journal of Mathematics
abstract:In this paper we investigate the differential geometric and algebro-geometric properties of the noncollapsing limit in the continuity method that was introduced by the first two authors.
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## References

SHOWING 1-10 OF 55 REFERENCES
Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry
• Mathematics
• 2014
We prove a general result about the geometry of holomorphic line bundles over Kähler manifolds.
A continuity method to construct canonical metrics
• Mathematics
• 2014
We introduce a new continuity method which, although less natural than flows such as the Kähler–Ricci flow, has the advantage of preserving a lower bound on the Ricci curvature, hence allowing the
Scalar Curvature Behavior for Finite Time Singularity of K
In this short paper, we show that K\"ahler-Ricci flows over closed manifolds would have scalar curvature blown-up for finite time singularity. Certain control of the blowing-up is achieved with some
On the Kähler-Ricci Flow on Projective Manifolds of General Type
• Mathematics
• 2006
This note concerns the global existence and convergence of the solution for Kähler-Ricci flow equation when the canonical class, KX, is numerically effective and big. We clarify some known results
Degeneration of Shrinking Ricci Solitons
Let (Y, d) be a Gromov-Hausdorff limit of closed shrinking Ricci solitons with uniformly upper bounded diameter and lower bounded volume. We prove that off a closed subset of codimension at least 2,
K-stability and K\"ahler-Einstein metrics
In this new version, we correct some typos. For the readers' convenience, we also added some footnotes and more details for certain lemmas and theorems.
The Kähler–Ricci flow through singularities
• Mathematics
• 2009
We prove the existence and uniqueness of the weak Kähler–Ricci flow on projective varieties with log terminal singularities. We also show that the weak Kähler–Ricci flow can be uniquely continued
On the singularities of spaces with bounded Ricci curvature
• Mathematics
• 2002
Abstract. ((Without Abstract)).