We prove that the moduli space of 2-convex embedded n-spheres in 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 metics on three-manifolds.

中文翻译：

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双凸嵌入球的模空间

我们证明了 R^{n+1} 中的 2 凸嵌入 n 球的模空间对于每个 n 都是路径连通的。我们的证明使用了手术的平均曲率流，可以看作是 Marques 对三流形上正标量曲率模数空间的路径连通性的有影响力证明的外在模拟。