Calabi conjecture and the complex Monge-Ampère equation

Author: Irakli Sikharulidze
Keywords: Kähler manifold, Kähler form, curvature, Ricci curvature tensor field, associated 2-form, Calabi conjecture, complex Monge-Ampère equation
Annotation:

The existence of an important kind of complex manifolds, the so called Calabi-Yau manifolds, relies on the Calabi conjecgture, which can be reduced to a complex Monge-Ampère equation, whose solution's existance and uniqueness was first demonstrated by Yau. Here are discussed notions and mathematical objects which are involved in the statement of the conjecture and those of their important properties are proven which allow the reduction of the conjecture to a complex Monge-Ampère equation.

Lecture files:

კალაბის ჰიპოთეზა და კომპლექსური მონჟ-ამპერის განტოლება [ka]