Logarithmic lower bound on the number of nodal domains
Spectral Theory
2016-12-22 v1
Abstract
We prove that the number of nodal domains of a density one subsequence of eigenfunctions grows at least logarithmically with the eigenvalue on negatively curved `real Riemann surfaces'. The geometric model is the same as in prior joint work with Junehyuk Jung (arXiv:1310.2919, to appear in J. Diff. Geom), where the number of nodal domains was shown to tend to infinity, but without a specified rate. The proof of the logarithmic rate uses the new logarithmic scale quantum ergodicity results of Hezari-Riviere (arXiv:1411.4078) and X. Han (arXiv:1410.3911).
Keywords
Cite
@article{arxiv.1510.05315,
title = {Logarithmic lower bound on the number of nodal domains},
author = {Steve Zelditch},
journal= {arXiv preprint arXiv:1510.05315},
year = {2016}
}