English

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

R2 v1 2026-06-22T21:24:36.455Z