The spectral gap of graphs and Steklov eigenvalues on surfaces

Q3 Mathematics

Electronic Research Announcements in Mathematical Sciences Pub Date : 2013-10-10 DOI:10.3934/era.2014.21.19

B. Colbois, A. Girouard

引用次数: 12

Abstract

Using expander graphs, we construct a sequence $\{\Omega_N\}_{N\in\mathbb{N}}$ of smooth compact surfaces with boundary of perimeter $N$, and with the first non-zero Steklov eigenvalue $\sigma_1(\Omega_N)$ uniformly bounded away from zero. This answers a question which was raised in [10]. The sequence $\sigma_1(\Omega_N) L(\partial\Omega_n)$ grows linearly with the genus of $\Omega_N$, which is the optimal growth rate.

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图的谱隙和曲面上的Steklov特征值

利用展开图，构造了一个光滑紧曲面序列$\{\Omega_N\}_{N\in\mathbb{N}}$，其边界周长为$N$，第一个非零Steklov特征值$\sigma_1(\Omega_N)$均匀有界远离零。这就回答了b[10]年提出的一个问题。序列$\sigma_1(\Omega_N) L(\partial\Omega_n)$与$\Omega_N$属线性生长，为最优生长速率。

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

Electronic Research Announcements in Mathematical Sciences 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication. ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007