Singularity analysis for manifolds with Ricci curvature bounds

具有 Ricci 曲率界的流形的奇异性分析

• 批准号: DE190101471
• 负责人: Prof Wenshuai Jiang
• 金额: $ 11.58万
• 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: 2019
• 资助国家: 澳大利亚
• 起止时间: 2019-06-19 至 2022-02-05
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE190101471
• 关键词: Singularity; analysis; manifolds; Ricci; curvature

This project aims to investigate the central problem of singularity analysis in manifolds by profiling their topological structures and analysing their geometric structure. Understanding the geometric structure of manifolds is at the forefront of research in geometry and topology, with applications in disciplines such as physics and medical imaging. The project will undertake pressing research in this active and dynamic field and expects to generate greater understanding of limit spaces, deepening the theory of geometric measure theory, and enhancing their applications in mathematics and science.

本计画旨在探讨流形奇异性分析的核心问题，借由描绘流形的拓扑结构及分析流形的几何结构。了解流形的几何结构是几何和拓扑学研究的前沿，在物理和医学成像等学科中有应用。该项目将在这一活跃和动态的领域进行紧迫的研究，并期望产生更好的理解极限空间，深化几何测度理论，并加强其在数学和科学中的应用。