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，这些界面被建模为由表面张力驱动的表面，可能在封闭的容器中。该项目预计将产生新的知识，在几何偏微分方程领域，通过利用新技术的几何流，并通过建立新的方法为边值问题。所开发的技术可能在数学分析的其他领域具有深远的应用，并且预期的结果将极大地有助于由平均曲率支配的表面理论，该理论出现在各种现实世界的现象中，例如肥皂泡、黑洞视界和火焰前沿。