In this article, we extend the mean curvature flow with surgery to mean convex hypersurfaces with entropy less than \(\varLambda _{n-2}\). In particular, 2-convexity is not assumed. Next we show the surgery flow with just the initial convexity assumption \(H - \frac{\langle x, \nu \rangle }{2} > 0\) is possible and as an application we use the surgery flow to show that smooth n-dimensional closed self shrinkers with entropy less than \(\varLambda _{n-2}\) are isotopic to the round n-sphere.

中文翻译：

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手术的低熵和平均曲率流

在本文中，我们通过手术将平均曲率流扩展到平均熵小于\（\ varLambda _ {n-2} \）的凸超曲面。特别地，不假定2-凸性。接下来，我们展示仅具有初始凸度假设\（H-\ frac {\ langle x，\ nu \ rangle} {2}> 0 \）的手术流程，并且作为一种应用，我们使用手术流程来证明平滑熵小于\（\ varLambda _ {n-2} \）的n维闭合自收缩器是圆形n球的同位素。