Non Compact Variational Problems in Contact Form Geometry and in Conformally Invariant Equations

接触形式几何和共形不变方程中的非紧变分问题

• 批准号: 0100672
• 负责人: Abbas Bahri
• 金额: $ 13.8万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-06-01 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0100672&HistoricalAwards=false
• 关键词: Non; Compact; Variational; Problems; Contact

I intend over the next three years to understand how hybrid objects, made partly of configurations spaces and partly of bary-center spaces and/or of a collection of unstable manifolds of critical points arise in Yamabe-type problems as well as in contact form geometry.I also would like to make out of the homology which I have defined for contact forms (on a space of dual Legendrian curves) a practical tool.Singular solutions arise in a natural way in several fields of Science (Physics: Ginsburg - Landau, liquid crystals, biology, chemistry etc). Smooth solutions are variational solutions which also arise in a natural way, in the same fields, but through a different process (extremization of kinetic plus potential energy in Physics...) I intend to understand at least partly what are the bridges connecting these two processes.

我打算在接下来的三年里了解混合物体，一部分由构形空间和一部分由重心空间和/或临界点的不稳定流形的集合构成，这些不稳定流形出现在Yamabe型问题和切触形式几何中。我还想利用我为切触形式定义的同调（在对偶勒让德曲线的空间上）一个实用的工具。奇异解以自然的方式出现在几个科学领域（物理学：金斯伯格-朗道，液晶，生物学，化学等）。光滑解是变分解，它也以自然的方式出现，在相同的领域，但通过不同的过程（物理学中动能加势能的极值化）。我打算至少部分地了解连接这两个过程的桥梁是什么。