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 .
Bibliographical noteFunding Information:
Acknowledgments. The authors have been supported by EPSRC grant EP/M011224/1, NSERC grant RGPIN-2016-04331, and NSF grant DMS-1406394. We thank Richard Bamler and Igor Belegradek for helpful discussions.
© 2021 International Press of Boston, Inc.. All rights reserved.