AI 中文总结
研究给定\(\mathbb{R}^{n + 1}\)中特定嵌入收缩子\(\Sigma\)，构造闭嵌入平均曲率流使其在首个奇点处切向流以\(\Sigma\)为模型并规定一阶渐近性，通过更一般定理实现，有附加力时也可构造。
AI 中文摘要
给定\(\mathbb{R}^{n + 1}\)中的一个嵌入收缩子\(\Sigma\)，它要么是闭的，渐近锥形的，要么是这样一个收缩子与\(\mathbb{R}^k\)的笛卡尔积，我们构造一个闭嵌入平均曲率流，其在第一个奇点处的切向流以\(\Sigma\)为模型。我们还规定了切向流的一阶渐近性。该结果是一个更一般定理的推论，该定理允许我们构造具有附加力的平均曲率流，其在第一个奇点处的切向流和一阶渐近性是规定的。
英文摘要
Given an embedded shrinker $Σ$ in $\mathbb{R}^{n+1}$ that is either closed, asymptotically conical, or a Cartesian product of such a shrinker with $\mathbb{R}^k$, we construct a closed embedded mean curvature flow whose tangent flow at the first singularity is modeled on $Σ$. We also prescribe the first-order asymptotics of the tangent flow. This result is a consequence of a more general theorem that allows us to construct mean curvature flows with an additional force whose tangent flow and first-order asymptotics at the first singularity are prescribed.
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