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math.CV2026
Regularity of rooftop envelopes
Eleonora Di Nezza, Alexander Rashkovskii
We study continuity, Hölder regularity, and -regularity of geodesics between continuous plurisubharmonic functions on bounded domains of . We then derive re…
math.CV2026
Families of singular Kähler-Einstein metrics
Eleonora Di Nezza, Vincent Guedj, Henri Guenancia
Refining Yau's and Kolodziej's techniques, we establish very precise uniform a priori estimates for degenerate complex Monge-Ampère equations on compact Kähler manifolds, that al…
math.CV2025
Singular Calabi-Yau metrics
Eleonora Di Nezza, Chinh H. Lu
These are notes of lectures given by the first named author during the CIME Summer school Calabi-Yau varieties. We survey known results concerning the complex Monge-Ampère equatio…