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Kähler families of Green's functions
Multi angle
Authors : Guedj, Vincent (Author of the conference)
CIRM (Publisher )
32U05 - plurisubharmonic functions and generalizations
32W20 - Complex Monge-Ampère operators
32Q15 - Kähler manifolds
35A23 - Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals
CIRM (Publisher )
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Abstract :
We establish uniform estimates for Green's functions associated to Kähler forms, as the latter evolve in large families and the complex structure varies. This generalizes works of Guo, Phong, Song, and Sturm. These estimates allow one to establish diameter bounds and non-collapsing estimates for various families of canonical Kähler metrics. This is joint work with T.D.Tô.
Keywords : Green's function; Monge-Ampère equation; a priori estimates
MSC Codes : Keywords : Green's function; Monge-Ampère equation; a priori estimates
32U05 - plurisubharmonic functions and generalizations
32W20 - Complex Monge-Ampère operators
32Q15 - Kähler manifolds
35A23 - Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals
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Information on the Video
Film maker : Récanzone, LucaLanguage : English Available date : 13/05/2025 Conference Date : 22/04/2025 Subseries : Research talks arXiv category : Complex Variables ; Algebraic Geometry ; Analysis of PDEs ; Differential Geometry Mathematical Area(s) : Geometry Format : MP4 (.mp4) - HD Video Time : 01:02:24 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-04-22_Guedj.mp4 
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Information on the Event
Event Title : Families of Kähler spaces / Familles d'espaces kählériensEvent Organizers : Cadorel, Benoît ; Cao, Junyan ; Deng, Ya ; Floris, Enrica ; Guenancia, Henri Dates : 21/04/2025 - 25/04/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3221.html
Citation Data
DOI : 10.24350/CIRM.V.20343203Cite this video as: Guedj, Vincent (2025). Kähler families of Green's functions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20343203 URI : http://dx.doi.org/10.24350/CIRM.V.20343203 |
See Also
- [Multi angle] Higgs bundles for Hecke eigensheaves in rank 2 and genus 2 / Author of the conference Simpson, Carlos.
- [Multi angle] A counter-example to the log-canonical Beauville-Bogomolov decomposition / Author of the conference Patakfalvi, Zsolt.
- [Multi angle] The Hassett-Keel program in genus 4 / Author of the conference Devleming, Kristin.
Bibliography
- GUEDJ, Vincent et TÔ, Tat Dat. Kähler families of Green's functions. Journal de l'École polytechnique — Mathématiques, Tome 12 (2025), pp. 319-339 - https://doi.org/10.5802/jep.291
Imagette Video
