Ariadna Leon Quiros: Hamilton's conjecture on Ricci-pinched three-manifolds via IMC

Abstract

Hamilton proved a pinching condition on the second fundamental form of submanifolds. He also conjectured an analogous pinching condition regarding the intrinsic curvatures of three-manifolds. This conjecture was proved via Ricci flow by the combination of several contributions. In this talk, I will introduce this proof via Ricci flow but I will mostly focus on showing the proof of this conjecture via IMCF (Inverse Mean Curvature Flow). The IMCF proof for this conjecture was first introduced by Huisken and Körber. Therefore, I will explain the main concepts of IMCF and show the details of this last mentioned proof.