古老而膨胀的自旋ALE Ricci流

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2025-05-27 DOI:10.1016/j.jfa.2025.111062

Isaac M. Lopez, Tristan Ozuch

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引用次数: 0

摘要

我们对自旋ALE古Ricci流和自旋ALE膨胀孤子在无穷远处的合适群进行了分类。特别是，SU(2)中唯一具有无穷远群的自旋古Ricci流和无穷远的轻微衰减是hyperkähler ALE度量。这个证明的主要思想，是一个独立的兴趣，在于证明佩雷尔曼μ泛函在任何非负标量曲率的ALE轨道上的大尺度行为是由一个与加权质量概念相关的重整化λALE泛函控制的。

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Ancient and expanding spin ALE Ricci flows

We classify spin ALE ancient Ricci flows and spin ALE expanding solitons with suitable groups at infinity. In particular, the only spin ancient Ricci flows with groups at infinity in

S U (2)

and mild decay at infinity are hyperkähler ALE metrics. The main idea of the proof, of independent interest, consists in showing that the large-scale behavior of Perelman's μ-functional on any ALE orbifold with non-negative scalar curvature is controlled by a renormalized

λ_{ALE}

-functional related to a notion of weighted mass.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis