AI 中文总结
研究富克斯流形中修正平均曲率流，证明其从任意图形出发始终存在，当\(t\to\infty\)时收敛到常平均曲率等距曲面，推广早期工作并去除标准平均曲率流的全局梯度界限制。
AI 中文摘要
本文表明，在富克斯流形中从任意图形出发的修正平均曲率流对所有时间都存在，并且当\(t\to\infty\)时平滑收敛到常平均曲率的等距曲面。该结果将早期工作推广到修正平均曲率流情形，去除了标准平均曲率流最初所需的严格全局梯度界。
英文摘要
In this paper, we show that the modified mean curvature flow starting from an arbitrary graph in a Fuchsian manifold exists for all time and converges smoothly to an equidistant surface of constant mean curvature as $t\to \infty$. This result generalizes earlier work to the modified mean curvature flow setting and removes the restrictive global gradient bound initially required for the standard mean curvature flow by Huang, Zhou, and the second author \cite{HLZ2020}.
Comments38 pages. Comments welcome!
