The moduli space of two-convex embedded spheres

Abstract

We prove that the moduli space of 2-convex embedded n-spheres in R^{n+1} is path-connected for every n. Our proof uses mean curvature flow with surgery and can be seen as an extrinsic analog to Marques' influential proof of the path-connectedness of the moduli space of positive scalar curvature metics on three-manifolds.

v2: We have revised the introduction to better reflect the similarities and differences between our work and related work in the intrinsic case by Marques (Ann. of Math. 2012)

Cited by in corpus (4)

• Mean curvature flow with surgery
• The moduli space of two-convex embedded tori
• Approximation of mean curvature flow with generic singularities by smooth flows with surgery
• Lectures on mean curvature flow of surfaces