自由边界流的定量规避及应用
Quantitative avoidance for free boundary flows and applications
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中文总结 AI 辅助
该研究引入扭曲费米距离，将自由边界Brakke流的规避原理推广至任意域，还把相关平均凸邻域定理等结果拓展到无凸性假设的任意域。
中文摘要 AI 辅助
本文中，我们引入了具有自由边界的超曲面之间的一种新距离函数，将其命名为扭曲费米距离（twisted Fermi distance），并证明该新量在带自由边界的平均曲率流下具有单调性。这克服了通常的距离函数在非凸域中可能丧失单调性的障碍，具有若干应用。最重要的是，我们将自由边界Brakke流的规避原理（该原理最近由第一作者针对凸域建立）推广到任意域。利用这一点，我们进而证明，我们近期合作工作中的所有结果，包括平均凸邻域定理和通过柱形奇点的自由边界流的唯一性定理，均可推广到任意域，且无需任何凸性假设。
英文摘要
In this article, we introduce a new distance function between hypersurfaces with free boundary. We show that our new quantity, which we call twisted Fermi distance, is monotone under mean curvature flow with free boundary. This overcomes the stumbling block that monotonicity of the usual distance function can fail for non-convex domains, and has several applications. Most importantly, we generalize the avoidance principle for free boundary Brakke flows, recently established by the first author for convex domains, to arbitrary domains. Using this, we then show that all results from our recent joint work, including the mean-convex neighborhood theorem and the uniqueness theorem for free boundary flows through cylindrical singularities, can be generalized to arbitrary domains without any convexity assumptions as well.
发表机构
- University of Toronto（多伦多大学）
机构由 AI 辅助整理，请以论文原文为准。
