正标量曲率度量的约束变形，2

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2023-09-07 DOI:10.1002/cpa.22153

Alessandro Carlotto, Chao Li

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引用次数: 4

摘要

证明了紧化三流形上约束正标量曲率度量的各种空间在不空的情况下是可收缩的。我们主要关注的约束是根据边界平均曲率的局部条件给出的，我们的处理包括平均凸和最小情况。然后讨论了这些结果对广义相对论中爱因斯坦场方程的渐近平坦初始数据集的不同子空间拓扑的意义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Constrained deformations of positive scalar curvature metrics, II

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Constrained deformations of positive scalar curvature metrics, II

We prove that various spaces of constrained positive scalar curvature metrics on compact three-manifolds with boundary, when not empty, are contractible. The constraints we mostly focus on are given in terms of local conditions on the mean curvature of the boundary, and our treatment includes both the mean-convex and the minimal case. We then discuss the implications of these results on the topology of different subspaces of asymptotically flat initial data sets for the Einstein field equations in general relativity.

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.