发表机构
Universität Augsburg（奥格斯堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一个普遍边界粘合原理，统一了Perelman、Gromov-Lawson和Bär-Hanke的经典粘合定理，并借助代数曲率锥和局部灵活性引理，证明了一个边界变形原理，用于比较不同边界条件下的度量空间。
AI 中文摘要
我们证明了一个关于黎曼度量族的普遍边界粘合原理，该度量族在可能具有非紧边界的流形上满足逐点曲率限制。作为特例，这包括了Perelman关于具有正Ricci曲率和凸奇点的度量的经典粘合定理，以及Gromov-Lawson和Bär-Hanke关于具有正标量曲率和平均凸奇点的度量的粘合定理。利用代数曲率锥的语言，我们的定理蕴含并统一了更多先前的粘合结果。我们还证明了一个边界变形原理，使我们能够比较具有内部曲率限制和不同边界条件的度量空间。我们的构造基于开放偏微分关系的局部灵活性引理，以及沿边界的显式1-jet度量变形。
英文摘要
We prove a general boundary gluing principle for families of Riemannian metrics with pointwise curvature restrictions on manifolds with possibly non-compact boundary. This includes, as special cases, the classical gluing theorems by Perelman for metrics with positive Ricci curvature and convex singularities and by Gromov-Lawson and Bär-Hanke for metrics with positive scalar curvature and mean convex singularities. Using the language of algebraic curvature cones, our theorem implies and unifies many more previous gluing results. We also prove a boundary deformation principle that enables us to compare spaces of metrics with interior curvature restrictions and different boundary conditions. Our construction is based on the local flexibility lemma for open partial differential relations, as well as explicit 1-jet deformations of metrics along the boundary.
Comments40 pages
