THE SPECTRAL GAP OF GRAPHS AND STEKLOV EIGENVALUES ON SURFACES

被引：9
|
作者：
Colbois, Bruno [1 ]
Girouard, Alexandre [2 ]
机构：
[1] Univ Neuchatel, Inst Math, CH-2009 Neuchatel, Switzerland
[2] Univ Laval, Dept Math & Stat, Quebec City, PQ G1V 0A6, Canada
来源：
ELECTRONIC RESEARCH ANNOUNCEMENTS IN MATHEMATICAL SCIENCES | 2014年 / 21卷
关键词：
Steklov problem; Riemannian surface; eigenvalue inequalities; expander graphs; COVERINGS; TOWER;
D O I：
10.3934/era.2014.21.19
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Using expander graphs, we construct a sequence {Omega(N)}N is an element of 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 PO]. The sequence sigma(1)(Omega(N))L(partial derivative Omega n) grows linearly with the genus of Omega(N), which is the optimal growth rate.
引用
收藏
页码：19 / 27
页数：9
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