Laplace operators with eigenfunctions whose nodal set is a knot

被引：1

作者：

Enciso, Alberto ^{[1
]}

Hartley, David ^{[1
]}

Peralta-Salas, Daniel ^{[1
]}

机构：

[1] CSIC, Inst Ciencias Matemat, Plaza Murillo 2, E-28049 Madrid, Spain

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2016年 / 271卷 / 01期

基金：

欧洲研究理事会;

关键词：

Eigenfunctions; Knots; Nodal set; GENERIC PROPERTIES;

D O I：

10.1016/j.jfa.2016.04.016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that, given any knot gamma in a compact 3-manifold M, there exists a Riemannian metric on M such that there is a complex-valued eigenfunction is of the Laplacian, corresponding to the first nontrivial eigenvalue, whose nodal set u(-1)(0) has a connected component given by gamma. Higher dimensional analogs of this result will also be considered. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：182 / 200

页数：19

共 19 条

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