The moduli space of two-convex embedded spheres

Reto Buzano, Robert Haslhofer, Or Hershkovits

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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].

Original languageAmerican English
Pages (from-to)189-221
Number of pages33
JournalJournal of Differential Geometry
Issue number2
StatePublished - Jun 2021
Externally publishedYes

Bibliographical note

Funding 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.

Publisher Copyright:
© 2021 International Press of Boston, Inc.. All rights reserved.


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