高属典型双曲面上的扭曲拉普拉奇谱分布

IF 2.2 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2024-06-23 DOI:10.1007/s00220-024-05027-1

Yulin Gong

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引用次数: 0

摘要

我们研究了高属典型双曲面上与均匀方整有界谐波 1 形相关的扭曲拉普拉斯函数的谱分布。首先，我们通过相应谐波形式的上顶规范来估计谱分布。随后，我们证明了对于典型的高属双曲面，可平方积分的有界谐波形式表现出较小的超顶规范。基于这些发现，我们证明了典型双曲面上谱实部分布的统一韦尔定律。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Spectral Distribution of Twisted Laplacian on Typical Hyperbolic Surfaces of High Genus

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Spectral Distribution of Twisted Laplacian on Typical Hyperbolic Surfaces of High Genus

We investigate the spectral distribution of the twisted Laplacian associated with uniform square-integrable bounded harmonic 1-form on typical hyperbolic surfaces of high genus. First, we estimate the spectral distribution by the supremum norm of the corresponding harmonic form. Subsequently, we show that the square-integrable bounded harmonic form exhibits a small supremum norm for typical hyperbolic surfaces of high genus. Based on these findings, we prove a uniform Weyl law for the distribution of real parts of the spectrum on typical hyperbolic surfaces.

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来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.