In this paper, we generalize White's regularity and structure theory for mean-convex mean curvature flow [45, 46, 48] to the setting with free boundary. A major new challenge in the free boundary setting is to derive an a priori bound for the ratio between the norm of the second fundamental form and the mean curvature. We establish such a bound via the maximum principle for a triple-approximation scheme, which combines ideas from Edelen [9], Haslhofer-Hershkovits [16], and Volkmann [43]. Other important new ingredients are a Bernstein-type theorem and a sheeting theorem for low-entropy free boundary flows in a half-slab, which allow us to rule out multiplicity 2 (half-)planes as possible tangent flows and, for mean-convex domains, as possible limit flows. © 2021 Wiley Periodicals LLC.

中文翻译：

---

具有自由边界的平均凸平均曲率流

在本文中，我们将 White 的平均凸平均曲率流 [45, 46, 48] 的规律性和结构理论推广到具有自由边界的设置。自由边界设置中的一个主要新挑战是推导出第二基本形式的范数与平均曲率之间的比率的先验界限。我们通过三重近似方案的最大原理建立了这样的界限，该方案结合了 Edelen [9]、Haslhofer-Hershkovits [16] 和 Volkmann [43] 的想法。其他重要的新成分是伯恩斯坦型定理和半板中低熵自由边界流动的薄片定理，这使我们能够排除多重性 2（半）平面作为可能的切线流动，并且对于平均凸域，尽可能限制流量。© 2021 威利期刊有限责任公司。