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H 1 Complex Monge-Ampere equations with prescribed singularities​

Auteurs : Di Nezza, Eleonora (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : 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

    Codes MSC :
    32J27 - Compact Kähler manifolds: generalizations, classification
    32Q20 - Kähler-Einstein manifolds
    32W20 - Complex Monge-Ampère operators
    32Q15 - Kähler manifolds

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 31/01/2018
      Date de captation : 18/01/2018
      Collection : Research talks ; Analysis and its Applications ; Partial Differential Equations ; Algebraic and Complex Geometry
      Format : MP4
      Durée : 00:54:19
      Domaine : Algebraic & Complex Geometry ; PDE ; Analysis and its Applications
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-01-18_DiNezza.mp4

    Informations sur la rencontre

    Nom de la rencontre : Constant scalar curvature metrics in Kähler and Sasaki geometry / Métriques à courbure scalaire constante en géométrie Kählérienne et Sasakienne
    Organisateurs de la rencontre : Auvray, Hugues ; Huang, Hongnian ; Keller, Julien ; Legendre, Eveline ; Sena-Dias, Rosa
    Dates : 15/01/2018 - 19/01/2018
    Année de la rencontre : 2018
    URL Congrès : https://conferences.cirm-math.fr/1750.html

    Citation Data

    DOI : 10.24350/CIRM.V.19263003
    Cite 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


    Voir aussi

    Bibliographie

    1. Darvas, T., Di Nezza, E., & Lu, C.H. (2017). Monotonicity of non-pluripolar products and complex Monge-Ampère equations with prescribed singularity. - https://arxiv.org/abs/1705.05796

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