Existence of extremal Kähler metrics on blowups

Apparaît dans la collection : Conférence à la mémoire de Jean-Pierre Demailly

Some 20 years ago, Arezzo and Pacard established that the existence of extremal Kähler metrics on a compact Kähler manifold is preserved under certain point blowups. This was later extended by Seyyadili-Szekelyhidi to blowups of certain higher dimensional submanifolds, and, quite recently, to the case of weighted extremal metrics, by Hallam. In this talk we present a new approach unifying both cases, based on the properness of the Mabuchi K-energy. This is joint work with Mattias Jonsson and Antonio Trusiani.