Ricci-flat metrics on Calabi-Yau manifolds

Abstract

We study the space of Ricci-flat Kahler metrics on a given Calabi-Yau manifold, pose a number of questions about their possible degenerations, and survey some recent results on these questions.

arXiv comment24 pages. To appear in the Proceedings of the ICM 2026

References in corpus (25)

• The Kähler-Ricci flow on surfaces of positive Kodaira dimension
• Adiabatic limits of Ricci-flat Kahler metrics
• Limits of Calabi-Yau metrics when the Kahler class degenerates
• The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits
• Gromov-Hausdorff collapsing of Calabi-Yau manifolds
• Collapsing of abelian fibred Calabi-Yau manifolds
• Kähler currents and null loci
• Infinite time singularities of the Kähler-Ricci flow
• Higher-order estimates for collapsing Calabi-Yau metrics
• Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy
• Collapsing hyperkähler manifolds
• Degenerations of Calabi-Yau metrics
• Triviality of fibered Calabi-Yau manifolds without singular fibers
• Calabi-Yau manifolds and their degenerations
• Smooth and Rough Positive Currents
• Canonical currents and heights for K3 surfaces
• Geometry of twisted Kähler-Einstein metrics and collapsing
• On the $4$-dimensional minimal model program for Kähler varieties
• Smooth asymptotics for collapsing Calabi-Yau metrics
• Collapsing Calabi-Yau fibrations and uniform diameter bounds
• Ricci-flat metrics and dynamics on K3 surfaces
• On $L^{\infty }$ estimates for Monge-Ampère and Hessian equations on nef classes
• Special Kähler geometry and holomorphic Lagrangian fibrations
• Collapsing immortal Kähler-Ricci flows
• Rigid currents on compact hyperkahler manifolds