Rigidity and boundary phenomena for geometric variational problems

几何变分问题的刚性和边界现象

• 批准号: DE230100415
• 负责人: Dr Jonathan Zhu
• 金额: --
• 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: 2023
• 资助国家: 澳大利亚
• 起止时间: 2023-01-01 至 2023-11-07
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE230100415
• 关键词: Rigidity; boundary; phenomena; geometric; variational

The proposed project aims to investigate theoretical properties of thin films and fluid interfaces, which are modelled as surfaces driven by surface tension, possibly in an enclosing container. This project is expected to generate new knowledge in the area of geometric partial differential equations, by utilising new techniques in geometric flows, and by establishing novel methods for boundary value problems. The developed techniques may have far-reaching applications in other areas of mathematical analysis, and the expected results would contribute greatly to the theory of surfaces governed by mean curvature, which arise in various real-world phenomena such as soap bubbles, black hole horizons and bushfire fronts.

拟议的项目旨在研究薄膜和流体界面的理论特性，这些特性可能是由表面张力驱动的表面，可能是在封闭的容器中。预计该项目将通过在几何流量中利用新技术，并通过建立新的边界价值问题方法来产生新知识。开发的技术可能在数学分析的其他领域中具有深远的应用，预期的结果将极大地促进由平均曲率支配的表面理论，这些表面是在各种现实现象中产生的，例如肥皂泡，黑洞地平线和灌木丛。