We show that the space of asymptotically conical self-expanders of the mean curvature flow is a smooth Banach manifold. An immediate consequence is that non-degenerate self-expanders—that is, those self-expanders that admit no non-trivial normal Jacobi fields that fix the asymptotic cone—are generic in a certain sense.

中文翻译：

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平均曲率流的渐近圆锥自膨胀空间

我们证明了平均曲率流的渐近锥形自膨胀空间是一个光滑的巴拿赫流形。一个直接的结果是非退化自扩展器——即那些不承认固定渐近锥的非平凡正规雅可比域的自扩展器——在某种意义上是泛型的。