Analysis on spaces with fibred cusps, II

具有纤维尖点的空间分析，II

• 批准号: 340035557
• 负责人: Professor Dr. Daniel Grieser
• 金额: --
• 依托单位: Institut für Mathematik (IFM)
• 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/340035557?language=en
• 关键词: Analysis; spaces; fibred; cusps; II

Fibred cusp metrics and their generalization, the iterated multiple fibred cusp metrics, are a class of complete Riemannian metrics which occur for example on locally symmetric spaces. The closely related (iterated multiple) fibred boundary metrics occur in many contexts of geometry and physics, e.g. Kähler geometry, Hilbert schemes and moduli spaces of monopoles.The goals of this project are to develop analytic tools for analyzing the natural geometric differential operators associated to these metrics and to apply these tools to questions of global analysis and spectral theory. Central to our approach is geometric microlocal analysis, and part of the project is to extend its scope and methods.

纤维尖点度量及其推广，迭代多纤维尖点度量，是一类例如出现在局部对称空间上的完备黎曼度量。紧密相关的(迭代多重)纤维边界度量存在于许多几何和物理环境中，例如Kähler几何、Hilbert格式和单分子模空间。本项目的目标是开发分析工具来分析与这些度量相关的自然几何微分算子，并将这些工具应用于整体分析和谱理论问题。我们方法的核心是几何微局部分析，该项目的一部分是扩展其范围和方法。