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Complex Brunn-Minkowski Theory and Uniqueness Theorems in Kähler Geometry

Offered By: BIMSA via YouTube

Tags

Complex Analysis Courses Differential Geometry Courses Convex Geometry Courses Kähler Geometry Courses

Course Description

Overview

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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.

Syllabus

Bo Berndtsson: Complex Brunn-Minkowski theory and some uniqueness theorems in Kähler... #ICBS2024


Taught by

BIMSA

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