Calculus of Variations and Geometric Measure Theory

R. Buzano - R. Haslhofer - O. Hershkovits

The moduli space of two-convex embedded spheres

created by muller on 12 Jun 2018
modified on 13 Jun 2022


Published Paper

Inserted: 12 jun 2018
Last Updated: 13 jun 2022

Journal: Journal of Differential Geometry
Volume: 118
Year: 2021
Doi: 10.4310/jdg/1622743139

ArXiv: 1607.05604 PDF


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.