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.
Citation
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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