Yau's conjecture

In differential geometry, Yau's conjecture is a mathematical conjecture which states that any closed Riemannian 3-manifold has an infinite number of smooth closed immersed minimal surfaces. It is named after Shing-Tung Yau, who posed it as the 88th entry in his 1982 list of open problems in differential geometry.

The conjecture was resolved by Kei Irie, Fernando Codá Marques and André Neves in the generic case, and by Antoine Song in full generality.