Perelman's conjecture for noncompact ancient three-dimensional Ricci flows

Let $(M,g(t))$ be a noncompact ancient $\kappa$-solution to the Ricci flow in dimension $3$ with positive curvature.

Perelman's conjecture. Then $(M,g(t))$ is the Bryant soliton.

This conjecture classifies the noncompact ancient $\kappa$-solutions with positive curvature. It was proved first in the class of steady gradient Ricci solitons and subsequently in full generality.