Geometric aspects of partial differential equations

偏微分方程的几何方面

• 批准号: 2274589
• 金额: --
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2274589
• 关键词: Geometric; aspects; partial; differential; equations

The key aim of Arjun's project is to investigate a selection of tentative conjectures concerning the behaviour of partial differential equations (PDE) that arise specifically in geometry. Such equations appear often to have properties that are much stronger than one would expect from generic PDE theory. One key objective within this research is to understand the well-posedness of mean curvature flow with very rough initial data. A completely novel methodology is being pursued in the lowest possible dimension, involving establishing sharp decay results for the length of curves undergoing curve shortening flow. Analogous results in Ricci flow over recent years have had profound implications in the study of differential geometry. The project fits into both the `Mathematical Analysis' and `Geometry and Topology' EPSRC research areas.

Arjun项目的主要目的是研究一系列关于偏微分方程（PDE）行为的尝试性理论，这些偏微分方程是在几何中特别出现的。这样的方程似乎经常有比一般偏微分方程理论所期望的更强的性质。本研究的一个关键目标是了解非常粗糙的初始数据的平均曲率流的适定性。一个全新的方法正在追求尽可能低的维度，包括建立急剧衰减的曲线长度经历曲线缩短流的结果。近年来，Ricci流的类似结果在微分几何的研究中有着深刻的意义。该项目既适合“数学分析”，也适合“几何和拓扑”EPSRC研究领域。