Boundary value problems and index theory on Riemannian and Lorentzian manifolds

黎曼和洛伦兹流形的边值问题和指数理论

• 批准号: 441731261
• 负责人: Professor Dr. Christian Bär
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/441731261?language=en
• 关键词: Boundary; value; problems; index; theory

Building on the results of the previous project “Index theory on Lorentzian manifolds” it is planned to investigate boundary value problems and index theory for first order operators in both the Riemannian and the Lorentzian setting. This emcompasses the derivation of geometric index formulas for general first-order elliptic operators on manifolds with boundary, relative index theory à la Gromov and Lawson, boundary value problems for non-compact and non-smooth boundary, higher index theory and Callias-type operators on the Riemannian side. On Lorentzian manifolds we investigate local index theory for Dirac-type and more general operators, initial-boundary value problems and the characteristic initial value problem for Dirac operators.

基于以前的项目“洛伦兹流形上的指数理论”的结果，计划研究黎曼和洛伦兹设置中一阶算子的边值问题和指数理论。这包括一般的一阶椭圆算子的几何指标公式的推导与边界流形，相对指标理论la Gromov和Lawson，非紧和非光滑边界的边值问题，高指标理论和Callias型算子的黎曼侧。在Lorentzian流形上，我们研究Dirac型和更一般的算子的局部指标理论，Dirac算子的初边值问题和特征初值问题。