渐近于西蒙斯锥的平均曲率流古解
Ancient mean curvature flow asymptotic to a minimal quadratic cone
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中文总结 AI 辅助
本文证明n≥5时，渐近于O(n)×O(n)对称西蒙斯锥且位于其一侧的平均曲率流古解在抛物区域内有唯一渐近行为，平均凸性假设下则完全唯一，且为Hardt-Simon叶状结构的定常流。
中文摘要 AI 辅助
本文证明，对于n≥5，一个光滑、适当嵌入且渐近于O(n)×O(n)对称西蒙斯锥、且位于该锥一侧的平均曲率流古解，在抛物区域内具有唯一渐近行为。当额外假设平均凸性时，可将唯一渐近行为升级为完全唯一性，并证明此类流必须是由Hardt-Simon叶状结构中的某一叶给出的定常流。
英文摘要
In this paper, we prove that a smooth, properly embedded ancient mean curvature flow that is asymptotic to an $O(n)\times O(m)$ symmetric minimal quadratic cone for $n +m \geq 10$, and lies on one side of the cone has to have unique asymptotics in the parabolic region. When additionally assuming mean convexity, we upgrade unique asymptotics to full uniqueness, and show that such flow has to be a stationary flow given by one of the leaves of the Hardt-Simon foliation. This is the first rigidity/unique asymptotics theory for ancient mean curvature flow with a $\textbf{singular minimal cone as the asymptotic model}$.
发表机构
- Rutgers University（罗格斯大学）
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