Calabi transformed the Calabi conjecture into a non–linear partial differential equation of complex Monge–Ampere type, and showed that this equation has at most one solution, thus establishing the uniqueness of the required Kähler metric.
Goldbach's conjecture | ''n''! conjecture | n! conjecture | Kato's conjecture | Calabi conjecture | Weil conjecture | ''Uncle Petros and Goldbach's Conjecture'' by Apostolos Doxiadis | Uncle Petros and Goldbach's Conjecture | Schanuel's conjecture | Pollock's conjecture | Mumford conjecture | Kepler conjecture | Heawood conjecture | Chang's conjecture | Catalan's conjecture | Blattner's conjecture | Beal's conjecture |
Shing-Tung Yau received the Fields Medal at the International Congress of Mathematicians in Warsaw in 1982 for his work in global differential geometry and elliptic partial differential equations, particularly for solving such difficult problems as the Calabi conjecture of 1954, and a problem of Hermann Minkowski in Euclidean spaces concerning the Dirichlet problem for the real Monge–Ampère equation.