Estimates for complex Monge-Ampère equations with small right hand side

Lundi 25 mars 14:00-15:00 - Valentino Tosatti - Northwestern University

Résumé : I will discuss three geometric situations where complex Monge-Ampère equations naturally appear with right hand side that is approaching zero. I will discuss estimates (or lack thereof) for these equations in each case, and their geometric significance : the optimal C^{1,1} regularity of geodesics in the space of Kähler metrics (joint with Chu and Weinkove), higher order C^k estimates for collapsing Calabi-Yau metrics (joint with Hein), and lack of higher regularity for Ricci-flat metrics on K3 surfaces coming from holomorphic dynamics (joint with Filip).

Lieu : IMO ; salle 3L8.

Estimates for complex Monge-Ampère equations with small right hand side  Version PDF