Complex Brunn-Minkowski Theory and Uniqueness Theorems in Kähler Geometry

Explore the intricacies of Complex Brunn-Minkowski theory and its applications in Kähler geometry in this 46-minute lecture presented at #ICBS2024. Delve into the fascinating world of complex counterparts to classical theorems in convex geometry, focusing on the replacement of volumes of convex bodies with L^2-norms of sections of holomorphic line bundles. Examine the case where the line bundle possesses only one ('constant') section, and discover how this perspective leads to groundbreaking generalizations of the Bando and Mabuchi uniqueness theorem for Kähler-Einstein metrics. Gain valuable insights into related results and expand your understanding of this complex mathematical field.