Minimal surfaces and singularities of mean curvature flow

该项目旨在描述变分理论中最小曲面的几何结构，并对平均曲率流的奇点进行分类。最小表面是肥皂膜的数学模型，其随时间变化的类似物是平均曲率流，这是一个动态过程，表面流动以尽可能快地减少其面积。最小曲面理论和平均曲率流理论是几何分析中的一个核心问题，已被证明是数学中一个强大而重要的工具。该项目预计将在平均曲率流的最小曲面和奇点分析方面产生新的重要结果，并增强在计算机视觉和概率等相关学科的潜在应用。

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.