Yau's conjecture

Yau's conjecture, proposed by mathematician Shing-Tung Yau, relates to the study of Kähler manifolds, particularly in the context of complex differential geometry and algebraic geometry. Specifically, it addresses the existence of Kähler metrics with specific curvature properties on complex manifolds. One of the notable forms of Yau's conjecture is concerned with the existence of Kähler-Einstein metrics on Fano manifolds.