A variational approach to the Yau–Tian–Donaldson conjecture
Robert J. Berman, Sébastien Boucksom, Mattias Jönsson
Abstract
We give a variational proof of a version of the Yau–Tian–Donaldson conjecture for twisted Kähler–Einstein currents, and use this to express the greatest (twisted) Ricci lower bound in terms of a purely algebro-geometric stability threshold. Our approach does not involve a continuity method or the Cheeger–Colding–Tian theory, and uses instead pluripotential theory and valuations. Along the way, we study the relationship between geodesic rays and non-Archimedean metrics.
Topics & Concepts
TianMathematicsConjectureGeodesicCalabi–Yau manifoldPure mathematicsStability (learning theory)EinsteinMathematical analysisMathematical physicsComputer scienceMachine learningLiteratureArtGeometry and complex manifoldsGeometric Analysis and Curvature FlowsAdvanced Algebra and Geometry