Sign and area in nodal geometry of Laplace eigenfunctions
| dc.creator | Nazarov, Fedor | |
| dc.creator | Polterovich, Leonid | |
| dc.creator | Sodin, Mikhail | |
| dc.date | 2004-02-25 | |
| dc.date | 2004-06-02 | |
| dc.date.accessioned | 2026-07-07T06:30:18Z | |
| dc.date.available | 2026-07-07T06:30:18Z | |
| dc.description | The paper deals with asymptotic nodal geometry for the Laplace-Beltrami operator on closed surfaces. Given an eigenfunction f corresponding to a large eigenvalue, we study local asymmetry of the distribution of sign(f) with respect to the surface area. It is measured as follows: take any disc centered at the nodal line {f=0}, and pick at random a point in this disc. What is the probability that the function assumes a positive value at the chosen point? We show that this quantity may decay logarithmically as the eigenvalue goes to infinity, but never faster than that. In other words, only a mild local asymmetry may appear. The proof combines methods due to Donnelly-Fefferman and Nadirashvili with a new result on harmonic functions in the unit disc. | |
| dc.description | 35 pages, improvement of presentation, refinement of the section on the Donnelly-Fefferman inequality | |
| dc.identifier | https://arxiv.org/abs/math/0402412 | |
| dc.identifier | http://arxiv.org/abs/math/0402412 | |
| dc.identifier | American Journal Math. 127 (2005), 879-910 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98308 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Complex Variables | |
| dc.subject | 35P20 | |
| dc.title | Sign and area in nodal geometry of Laplace eigenfunctions | |
| dc.type | text |