Nodal lengths of eigenfunctions in the disc

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.

arXiv comment10 pages. Typos have been corrected in the second version

References in corpus (1)

• Lower bounds for nodal sets of eigenfunctions

Cited by in corpus (1)

• On exact Pleijel's constant for some domains