SPP 1154: Global Differential Geometry

优先项目支持全球黎曼几何、几何分析和辛几何的项目，特别强调这些研究领域之间的相互作用。全局黎曼几何涵盖了有关几何结构的全局问题：例如，具有规定曲率的度量或低维流形上的几何结构的存在性和阻塞性结果。使用的典型方法包括几何极限、渐近对称和同伦原理。此外，扩展光滑黎曼几何的框架，具有曲率边界的奇异空间几何是该项目的一部分。该计划的几何分析部分的主要主题是黎曼几何中椭圆算子的谱几何（包括在微分拓扑中的应用），洛伦兹流形的几何和分析（以及与之相关的）以及常平均曲率子流形的分析。辛几何处理与辛不变量、哈密顿动力系统、拉格朗日子流形和奇维流形上的接触结构有关的问题。

The Priority Programme supports projects in Global Riemannian Geometry, Geometric Analysis and Symplectic Geometry with a particular emphasize on interaction between these research areas.Global Riemannian Geometry covers global problems concerning geometric structures: for instance existence and obstruction results for metrics with prescribed curvature or geometric structures on low-dimensional manifolds. Typical methods used include geometric limits, asymptotic symmetry and homotopy principles. Also, extending the frame of smooth Riemannian geometry, the geometry of singular spaces with curvature bounds is part of the project. The main topics of the Geometric Analysis part of the programme are the spectral geometry of elliptic operators in Riemannian geometry (including applications in differential topology), the geometry and analysis on (and related to) Lorentzian manifolds and the analysis of submanifolds of constant mean curvature. Symplectic Geometry treats questions related to symplectic invariants, Hamiltonian dynamical systems, Lagrangian submanifolds and contact structures on odd-dimensional manifolds.