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June 2021 The moduli space of two-convex embedded spheres
Reto Buzano, Robert Haslhofer, Or Hershkovits
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J. Differential Geom. 118(2): 189-221 (June 2021). DOI: 10.4310/jdg/1622743139

Abstract

We prove that the moduli space of $2$-convex embedded $n$-spheres in $\mathbb{R}^{n+1}$ 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 metrics on three-manifolds.

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Reto Buzano. Robert Haslhofer. Or Hershkovits. "The moduli space of two-convex embedded spheres." J. Differential Geom. 118 (2) 189 - 221, June 2021. https://doi.org/10.4310/jdg/1622743139

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Received: 23 January 2017; Published: June 2021
First available in Project Euclid: 3 June 2021

Digital Object Identifier: 10.4310/jdg/1622743139

Rights: Copyright © 2021 Lehigh University

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Vol.118 • No. 2 • June 2021
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