Singularity analysis for ricci flow and mean curvature flow

里奇流和平均曲率流的奇异性分析

• 批准号: DE180101348
• 负责人: Dr Haotian Wu
• 金额: $ 22.96万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2018
• 资助国家: 澳大利亚
• 起止时间: 2018-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE180101348
• 关键词: Singularity; analysis; ricci; flow; mean

This project aims to investigate the central problem of singularity formation in Ricci flow and mean-curvature flow by profiling singular solutions and determining their stability and genericity. Geometric flows are powerful and successful ways of understanding classical problems in geometry and topology with applications in disciplines such as materials science and medical imaging. This project will generate significant results in singularity analysis and will enrich understanding of geometric flows at and past singularities, deepen the theory of geometric flows, and enhance their applications in mathematics and science.

本项目旨在研究里奇流和平均曲率流奇异解形成的中心问题，并确定其稳定性和一般性。在材料科学和医学成像等学科中，几何流是理解几何和拓扑经典问题的强大而成功的方法。本项目将在奇点分析方面取得重要成果，丰富人们对奇点处和过去的几何流动的认识，深化几何流动理论，增强其在数学和科学中的应用。