Minimal surfaces and singularities of mean curvature flow

该项目旨在刻画变分理论中极小曲面的几何结构，并对平均曲率流的奇点进行分类。极小表面是肥皂膜的数学模型，其随时间变化的模拟是平均曲率流，即表面流动以尽可能快地减小其面积的动态过程。作为几何分析的中心课题，极小曲面和平均曲率流理论已被证明是数学中一个强大而重要的工具。该项目有望在平均曲率流的最小曲面和奇异性分析方面产生新的和重要的结果，并增强在计算机视觉和概率等相关学科中的潜在应用。

The project aims to characterise the geometric structure of minimal surfaces in the variational theory and classify singularities of mean curvature flow. Minimal surfaces are mathematical models of soap films, and their time-varying analogue is mean curvature flow, a dynamic process by which a surface flows to decrease its area as quickly as possible. As a central topic in geometric analysis, the theory of minimal surfaces and mean curvature flow has proven to be a powerful and essential tool in mathematics. The project expects to generate new and significant results in minimal surfaces and singularity analysis of mean curvature flow and enhance potential applications in related disciplines such as computer vision and probability.