Constructions of Uniformly Positive Scalar Curvature Metrics on Open Manifolds
发布时间：2026年11月11日
浏览次数：7
发布者: He Liu
主讲人： Anushree Das（数学中心）
活动时间： 从 2026-11-13 15:00 到 16:00
场地： 北京国际数学研究中心，镜春园78号院（怀新园）77201室
A complete Riemannian metric has uniformly positive scalar curvature if its scalar curvature is bounded below by a positive constant. While the existence of positive scalar curvature metrics on closed manifolds is quite well understood, the corresponding questions on open manifolds are considerably more subtle. In this talk, we will see several sufficient conditions for an open manifold to admit a complete metric of uniformly positive scalar curvature, together with explicit constructions of such metrics. These include manifolds of dimension n ≥ 3 admitting a proper Morse function, bounded below, with no critical points of index at least n − 2; manifolds of dimension 3≤ n ≤ 7 with a positive scalar curvature metric and a compact exhaustion with minimal boundaries; and manifolds with product ends carrying a positive scalar curvature metric with suitable quadratic decay and a mean convex slice far enough out. Finally, we will discuss some applications of these constructions by others, including to questions of Gromov on the existence of uniformly positive scalar curvature metrics.
