Yau's conjecture

Not to be confused with Yau's conjecture on the first eigenvalue.

In differential geometry, Yau's conjecture is a mathematical conjecture which states that any closed Riemannian 3-manifold has infinitely many 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.^[1]

The conjecture was resolved by Kei Irie, Fernando Codá Marques and André Neves in the generic case,^[2] and by Antoine Song in full generality.^[3]