光滑度量空间中紧凑超曲面的指数估算

IF 1.3 3区数学 Q1 MATHEMATICS Proceedings of the Royal Society of Edinburgh Section A-Mathematics Pub Date : 2024-03-07 DOI:10.1017/prm.2024.25

Márcio Batista, Matheus B. Martins

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引用次数: 0

摘要

在这篇文章中，我们研究了作为超曲面沉浸在光滑度量空间（可能有奇点）中的紧凑流形上的稳定性算子和霍奇-拉普拉斯算子的谱。利用罗斯（A. Ros）和萨沃（A. Savo）提出的观点以及一种巧妙的计算方法，我们获得了这些算子谱之间的比较。作为这一技术的副产品，我们推导出了此类超曲面的莫尔斯指数的估计值。

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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Index estimates of compact hypersurfaces in smooth metric measure spaces

In this article, we investigate the spectra of the stability and Hodge–Laplacian operators on a compact manifold immersed as a hypersurface in a smooth metric measure space, possibly with singularities. Using ideas developed by A. Ros and A. Savo, along with an ingenious computation, we have obtained a comparison between the spectra of these operators. As a byproduct of this technique, we have deduced an estimate of the Morse index of such hypersurfaces.

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来源期刊

Proceedings of the Royal Society of Edinburgh Section A-Mathematics 数学-数学

CiteScore

3.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： A flagship publication of The Royal Society of Edinburgh, Proceedings A is a prestigious, general mathematics journal publishing peer-reviewed papers of international standard across the whole spectrum of mathematics, but with the emphasis on applied analysis and differential equations. An international journal, publishing six issues per year, Proceedings A has been publishing the highest-quality mathematical research since 1884. Recent issues have included a wealth of key contributors and considered research papers.