A note on the long neck principle and spectral width inequality of geodesic collar neighborhoods

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-03-29 DOI:10.1090/proc/16869

Daoqiang Liu

引用次数: 0

Abstract

The main purpose of this short note is to derive some generalizations of the long neck principle and give a spectral width inequality of geodesic collar neighborhoods. Our results are obtained via the spinorial Callias operator approach. An important step is to introduce the relative Gromov-Lawson pair on a compact manifold with boundary, relative to a background manifold.

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关于大地领邻域的长颈原理和谱宽不等式的说明

这篇短文的主要目的是推导长颈原理的一些概括，并给出大地领邻域的谱宽不等式。我们的结果是通过自旋卡利亚斯算子方法得到的。其中重要的一步是在有边界的紧凑流形上引入相对于背景流形的相对格罗莫夫-劳森对。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.