Two Calabi-Yau Theorems for Degenerations of Compact Kahler Manifolds

Paper in proceeding, 2026

We discuss two closely related Calabi-Yau theorems for degenerations of compact Kahler manifolds. The first is a Calabi-Yau theorem for big test configurations. The second result is a Calabi-Yau theorem for a wider class of degenerations, formulated in the language of non-Archimedean Kahler geometry. This theorem was first proved in the algebraic setting by Boucksom-Jonsson, while Mesquita-Piccione and I recently proved the general Kahler case. Our main focus here is on the connection between these results and the theory of big cohomology classes and their volumes.