Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds

我们研究了紧、非紧和奇异流形上的黎曼度量。一方面，微分几何中的重要问题涉及具有特定曲率性质的(完备)度量的存在和构造。另一方面，存在问题的解决推动了对所有这类度量空间的研究。在这个项目中，我们将主要处理具有较低标量、Ricci和截面曲率界限的度量。我们的目标是更好地理解这种度量的空间和模空间的结构和拓扑性质。

We investigate Riemannian metrics on compact, non-compact and singular manifolds. On the one hand, important questions in differential geometry concern the existence and construction of (complete) metrics with specific curvature properties. On the other hand, the solution of the existence question motivates the study of the space of all such metrics. In this project we will mainly be dealing with metrics with lower scalar, Ricci and sectional curvature bounds. The goal is an improved understanding of the structure and of the topological properties of spaces and moduli spaces of such metrics.