The moduli space of two-convex embedded spheres

Reto Buzano; Robert Haslhofer; Or Hershkovits

doi:10.4310/jdg/1622743139

The moduli space of two-convex embedded spheres

Reto Buzano, Robert Haslhofer, Or Hershkovits

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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].

Original language	American English
Pages (from-to)	189-221
Number of pages	33
Journal	Journal of Differential Geometry
Volume	118
Issue number	2
DOIs	https://doi.org/10.4310/jdg/1622743139
State	Published - Jun 2021
Externally published	Yes

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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author = "Reto Buzano and Robert Haslhofer and Or Hershkovits",

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: {\textcopyright} 2021 International Press of Boston, Inc.. All rights reserved.",

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AU - Hershkovits, Or

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AB - 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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The moduli space of two-convex embedded spheres

Abstract

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