Metric limits of Calabi-Yau manifolds

Mercredi 7 mars 14:00-17:00 - Valentino Tosatti - Northwestern

Résumé : I will give an introduction to the study of limits of Ricci-flat Kahler metrics on a compact Calabi-Yau manifold when the Kahler class degenerates to the boundary of the Kahler cone. Analytically, the problem is to prove suitable uniform a priori estimates for solutions of a degenerating family complex Monge-Ampère equations, away from some singular set. Geometrically, this can be used to understand the Gromov-Hausdorff limit of these metrics. I will discuss some results on this problem, obtained with various coauthors, in both the noncollapsing case and in the much harder collapsing case.

Lieu : Salle 3L8

Metric limits of Calabi-Yau manifolds  Version PDF