Minimal surfaces and singularities of mean curvature flow

平均曲率流的最小曲面和奇点

• 批准号: DE210100535
• 负责人: Dr Qiang Guang
• 金额: $ 9.26万
• 依托单位: The Australian National University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2021
• 资助国家: 澳大利亚
• 起止时间: 2021-02-01 至 2023-10-23
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE210100535
• 关键词: Minimal; surfaces; singularities; mean; curvature

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.

该项目的目的是在变分理论中描述极小曲面的几何结构，并对平均曲率流的奇异性进行分类。 最小表面是肥皂膜的数学模型，它们随时间变化的类似物是平均曲率流，这是一个动态过程，通过该过程，表面流动以尽可能快地减少其面积。作为几何分析中的一个中心课题，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。该项目预计将在极小曲面和平均曲率流的奇异性分析方面产生新的重要成果，并增强计算机视觉和概率等相关学科的潜在应用。