# 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} }

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.

## 16 Citations

Bounding Diameter of Conical Kähler Metric

- Mathematics
- 2015

In this paper we research the differential geometric and algebro-geometric properties of the noncollapsing limit in the conical continuity equation which generalize the theory in La Nave et al. in…

The continuity method on Fano bundles

- Mathematics
- 2016

We prove that the continuity method on a Fano bundle starting from a suitable K\"ahler metric converges to a K\"ahler metric on the base in Gromov-Hausdorff topology.

DEGENERATION OF RICCI-FLAT CALABI-YAU MANIFOLDS AND ITS APPLICATIONS

- Mathematics
- 2015

This is a survey article of the recent progresses on the metric behaviour of Ricci-flat K\"{a}hler-Einstein metrics along degenerations of Calabi-Yau manifolds.

The continuity equation with cusp singularities

- MathematicsMathematische Annalen
- 2018

In this paper we study a special case of the completion of cusp Kähler–Einstein metric on the regular part by taking the continuity method proposed by La Nave and Tian. The differential geometric and…

The continuity method on minimal elliptic K\"ahler surfaces

- Mathematics
- 2016

We prove that, on a minimal elliptic Kahler surface of Kodaira dimension one, the continuity method introduced by La Nave and Tian in \cite{LT} starting from any initial Kahler metric converges in…

The continuity equation of almost Hermitian metrics

- Mathematics
- 2021

Abstract We extend the continuity equation of the Kahler metrics introduced by La Nave & Tian and the Hermitian metrics introduced by Sherman & Weinkove to the almost Hermitian metrics, and establish…

Geometric estimates for complex Monge–Ampère equations

- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2020

Abstract We prove uniform gradient and diameter estimates for a family of geometric complex Monge–Ampère equations. Such estimates can be applied to study geometric regularity of singular solutions…

EXISTENCE OF KÄHLER-RICCI SOLITONS ON SMOOTHABLE Q-FANO VARIETIES

- 2019

In this article we prove the existence of Kähler-Ricci solitons on smoothable, K-stable Q-Fano varieties. We also investigate the behavior of twisted Kähler-Ricci solitons in the Gromov-Hausdorff…

The Continuity Method on Fano Fibrations

- MathematicsInternational Mathematics Research Notices
- 2018

We study finite-time collapsing limits of the continuity method. When the continuity method starting from a rational initial Kahler metric on a projective manifold encounters a finite-time volume…

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