Nodal lengths of eigenfunctions in the disc
Analysis of PDEs
2017-09-26 v2 Spectral Theory
Abstract
In this paper, we derive the sharp lower and upper bounds of nodal lengths of Laplacian eigenfunctions in the disc. Furthermore, we observe a geometric property of the eigenfunctions whose nodal curves maximize the nodal length.
Keywords
Cite
@article{arxiv.1708.08112,
title = {Nodal lengths of eigenfunctions in the disc},
author = {Xiaolong Han and Michael Murray and Chuong Tran},
journal= {arXiv preprint arXiv:1708.08112},
year = {2017}
}
Comments
10 pages. Typos have been corrected in the second version