It is known that any closed surface possesses infinitely many
closed geodesics. The first problem in the minimal submanifolds section of
Yau's list (
Yau's conjecture) asks whether any closed
three-manifold has infinitely many closed smooth
immersed minimal surfaces. At the time it was known from
Almgren–Pitts min-max theory the existence of at least one minimal surface. Kei Irie,
Fernando Codá Marques, and
André Neves solved this problem in the
generic case and later Song proved it in full generality. Together with Conghan Dong, he proved a conjecture from 2001 by
G. Huisken and
T. Ilmanen on the mathematics of
general relativity, about the
curvature in spaces with very little
mass. ==Honours and awards==