A transcendental non-Archimedean Calabi–Yau Theorem with applications to the cscK problem

This paper is joint with David Witt Nyström.

We solve the non-Archimedean Monge-Ampère equation for compact Kähler manifolds, generalizing a result of Boucksom–Favre–Jonsson to the transcendental setting. This allows us to derive a valuative criterion for uniform K-stability for models. As a central application, we prove that this stability condition implies the existence of a unique constant scalar curvature Kähler metric.

Recommended citation: P. Mesquita-Piccione, D, Witt Nyström (2025). "A transcendental non-Archimedean Calabi--Yau Theorem with applications to the cscK problem." Preprint, arXiv:2509.09442 [math.AG].
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