scholarly journals HIGHER ORDER ASYMPTOTIC BEHAVIOR OF CERTAIN KÄHLER METRICS AND UNIFORMIZATION FOR STRONGLY PSEUDOCONVEX DOMAINS

2015 ◽  
Vol 52 (1) ◽  
pp. 113-124 ◽  
Author(s):  
Jae-Cheon Joo ◽  
Aeryeong Seo
Keyword(s):  
Asymptotic Behavior ◽  
Higher Order ◽  
Pseudoconvex Domains ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Strongly Pseudoconvex Domains

scholarly journals Existence of complete Kähler Ricci-flat metrics on crepant resolutions

2014 ◽  
Vol 16 (03) ◽  
pp. 1450003 ◽  
Author(s):  
Bianca Santoro
Keyword(s):  
Asymptotic Behavior ◽  
Existence Results ◽  
Kähler Metrics ◽  
Asymptotically Flat ◽  
Kahler Metrics ◽  
Ricci Flat ◽  
Crepant Resolutions ◽  
Flat Metric

In this note, we obtain existence results for complete Ricci-flat Kähler metrics on crepant resolutions of singularities of Calabi–Yau varieties. Furthermore, for certain asymptotically flat Calabi–Yau varieties, we show that the Ricci-flat metric on the resolved manifold has the same asymptotic behavior as the initial variety.

scholarly journals Geometry and topology of the space of Kähler metrics on singular varieties

2018 ◽  
Vol 154 (8) ◽  
pp. 1593-1632 ◽  
Author(s):  
Eleonora Di Nezza ◽  
Vincent Guedj
Keyword(s):  
Einstein Metrics ◽  
Normal Space ◽  
Fano Varieties ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Metric Properties ◽  
Singular Varieties ◽  
Underlying Space ◽  
And Topology ◽  
Kähler Einstein Metrics

Let $Y$ be a compact Kähler normal space and let $\unicode[STIX]{x1D6FC}\in H_{\mathit{BC}}^{1,1}(Y)$ be a Kähler class. We study metric properties of the space ${\mathcal{H}}_{\unicode[STIX]{x1D6FC}}$ of Kähler metrics in $\unicode[STIX]{x1D6FC}$ using Mabuchi geodesics. We extend several results of Calabi, Chen, and Darvas, previously established when the underlying space is smooth. As an application, we analytically characterize the existence of Kähler–Einstein metrics on $\mathbb{Q}$-Fano varieties, generalizing a result of Tian, and illustrate these concepts in the case of toric varieties.

scholarly journals Adiabatic limits of Ricci-flat Kähler metrics

2010 ◽  
Vol 84 (2) ◽  
pp. 427-453 ◽  
Author(s):  
Valentino Tosatti
Keyword(s):  
Kähler Metrics ◽  
Kahler Metrics ◽  
Adiabatic Limits ◽  
Ricci Flat

scholarly journals Bianchi type A hyper-symplectic and hyper-Kähler metrics in 4D

2011 ◽  
Vol 29 (2) ◽  
pp. 025003 ◽  
Author(s):  
L C de Andrés ◽  
M Fernández ◽  
S Ivanov ◽  
J A Santisteban ◽  
L Ugarte ◽  
...  
Keyword(s):  
Bianchi Type ◽  
Type A ◽  
Kähler Metrics ◽  
Kahler Metrics
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