We prove that the moduli space of 2-convex embedded n-spheres in Rn+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 metrics on three-manifolds [21].
The moduli space of two-convex embedded spheres
Buzano R.;
2021-01-01
Abstract
We prove that the moduli space of 2-convex embedded n-spheres in Rn+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 metrics on three-manifolds [21].
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Two-Convex Spheres (JDG 2021).pdf
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