Higher order curvature flow of curves and hypersurfaces

曲线和超曲面的高阶曲率流

• 批准号: DP150100375
• 负责人: Prof James McCoy
• 金额: $ 31.12万
• 依托单位: The University of Newcastle
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2015
• 资助国家: 澳大利亚
• 起止时间: 2015-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP150100375
• 关键词: Higher; order; curvature; flow; curves

This project aims to analyse higher order geometric partial differential equations that have important mathematical applications in differential geometry of submanifolds as well as practical applications in physics and mathematical biology. The project aims to prove new general principles that reveal properties of these higher order elliptic and parabolic partial differential equations, producing a unified framework with applications to various specific problems. This project aims to increase Australia's research capacity in geometric evolution problems, provide training for some of Australia's next generation of mathematicians and build Australia's international reputation for significant research in geometric analysis.

该项目旨在分析高阶几何偏微分方程，这些方程在子流形微分几何中具有重要的数学应用，并且在物理学和数学生物学中具有实际应用。该项目旨在证明新的一般原理，揭示这些高阶椭圆和抛物型偏微分方程的性质，产生一个适用于各种具体问题的统一框架。该项目旨在提高澳大利亚在几何演化问题方面的研究能力，为澳大利亚一些下一代数学家提供培训，并建立澳大利亚在几何分析重大研究方面的国际声誉。