Periodic manifolds, spectral gaps, and eigenvalues in gaps

被引：0
|
作者：
Post, O [1 ]
机构：
[1] Rhein Westfal TH Aachen, Inst Reine & Angew Math, D-52062 Aachen, Germany
来源：
PARTIAL DIFFERENTIAL EQUATIONS AND SPECTRAL THEORY | 2001年 / 126卷
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D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate spectral properties of the Laplace operator on a class of non-compact Riemannian manifolds. We prove that for a given number N we can construct a periodic manifold such that the essential spectrum of the corresponding Laplacian has at least N open gaps. Furthermore, by perturbing the periodic metric of the manifold locally we can prove the existence of eigenvalues in a gap of the essential spectrum.
引用
收藏
页码：251 / 260
页数：10
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