A variational approach to the Yau-Tian-Donaldson conjecture

Robert Berman, Sébastien Boucksom, Mattias Jonsson

Published 2015-09-15Version 1

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.