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Complex Monge-Ampere equations with prescribed singularities
Multi angle
Authors : Di Nezza, Eleonora (Author of the conference)
CIRM (Publisher )
32J27 - Compact Kähler manifolds: generalizations, classification
32Q20 - Kähler-Einstein manifolds
32W20 - Complex Monge-Ampère operators
32Q15 - Kähler manifolds
CIRM (Publisher )
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Abstract :
Since the proof of the Calabi conjecture given by Yau, complex Monge-Ampère equations on compact Kähler manifolds have been intensively studied.
In this talk we consider complex Monge-Ampère equations with prescribed singularities. More precisely, we fix a potential and we show existence and uniqueness of solutions of complex Monge-Ampère equations which have the same singularity type of the model potential we chose. This result can be interpreted as a generalisation of Yau's theorem (in this case the model potential is smooth).
As a corollary we obtain the existence of singular Kähler-Einstein metrics with prescribed singularities on general type and Calabi-Yau manifolds.
This is a joint work with Tamas Darvas and Chinh Lu.
Keywords : complex Monge-Ampère equations; compact Kähler manifolds; singularities; Kähler-Einstein metrics; Calabi-Yau manifolds
MSC Codes : In this talk we consider complex Monge-Ampère equations with prescribed singularities. More precisely, we fix a potential and we show existence and uniqueness of solutions of complex Monge-Ampère equations which have the same singularity type of the model potential we chose. This result can be interpreted as a generalisation of Yau's theorem (in this case the model potential is smooth).
As a corollary we obtain the existence of singular Kähler-Einstein metrics with prescribed singularities on general type and Calabi-Yau manifolds.
This is a joint work with Tamas Darvas and Chinh Lu.
Keywords : complex Monge-Ampère equations; compact Kähler manifolds; singularities; Kähler-Einstein metrics; Calabi-Yau manifolds
32J27 - Compact Kähler manifolds: generalizations, classification
32Q20 - Kähler-Einstein manifolds
32W20 - Complex Monge-Ampère operators
32Q15 - Kähler manifolds
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 31/01/2018 Conference Date : 18/01/2018 Subseries : Research talks arXiv category : Differential Geometry ; Analysis of PDEs ; Complex Variables Mathematical Area(s) : Algebraic & Complex Geometry ; PDE ; Analysis and its Applications Format : MP4 (.mp4) - HD Video Time : 00:54:19 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-01-18_DiNezza.mp4 
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Information on the Event
Event Title : Constant scalar curvature metrics in Kähler and Sasaki geometry / Métriques à courbure scalaire constante en géométrie Kählérienne et SasakienneEvent Organizers : Auvray, Hugues ; Huang, Hongnian ; Keller, Julien ; Legendre, Eveline ; Sena-Dias, Rosa Dates : 15/01/2018 - 19/01/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1750.html
Citation Data
DOI : 10.24350/CIRM.V.19263003Cite this video as: Di Nezza, Eleonora (2018). Complex Monge-Ampere equations with prescribed singularities. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19263003 URI : http://dx.doi.org/10.24350/CIRM.V.19263003 |
See Also
- [Post-edited] Variational and non-Archimedean aspects of the Yau-Tian-Donaldson conjecture / Author of the conference Boucksom, Sébastien.
- [Multi angle] Extremal Poincaré type metrics and stability of pairs on Hirzebruch surfaces / Author of the conference Sektnan, Lars Martin.
- [Multi angle] Kähler-Ricci solitons on crepant resolutions of finite quotients of $C^n$ / Author of the conference Macbeth, Heather.
Bibliography
- Darvas, T., Di Nezza, E., & Lu, C.H. (2017). Monotonicity of non-pluripolar products and complex Monge-Ampère equations with prescribed singularity.
