A VARIATIONAL APPROACH TO THE YAU-TIAN-DONALDSON CONJECTURE

Robert Berman (1) , Sébastien Boucksom (2) , Mattias Jonsson (3)

1 Chalmers - Department of Mathematical Sciences
2 CMLS - Centre de Mathématiques Laurent Schwartz
3 Department of Mathematics

We give a new proof of a uniform version of the Yau-Tian-Donaldson conjecture for Fano manifolds with finite automorphism group, and of the semistable case of the conjecture. Our approach does not involve the continuity method or Cheeger-Colding-Tian theory. Instead, the proof is variational and uses pluripotential theory and certain non-Archimedean considerations.

Domaines: Mathématiques [math]

Robert Berman, Sébastien Boucksom, Mattias Jonsson. A VARIATIONAL APPROACH TO THE YAU-TIAN-DONALDSON CONJECTURE. 2018. ⟨hal-01708674⟩