Pleijel's nodal domain theorem for free membranes
By Iosif Polterovich. 2008
64 citations recorded by the source corpus.
We prove an analogue of Pleijel's nodal domain theorem for piecewise analytic planar domains with Neumann boundary conditions. This confirms a conjecture made by Pleijel in 1956. The proof is a combination of Pleijel's original approach and an estimate due to Toth and Zelditch for the number of boundary zeros of Neumann eigenfunctions.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ffbc770e49ae44be5c4067449ad09a9871fa2070
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In Applied Mathematics
- Steve Zelditch
- Jean Bourgain
- Larry Guth
- Jean Van Schaftingen
- Jonathan Bennett
- Christopher D. Sogge
- Zhiqin Lu
- Ciprian Demeter
In Mathematical Physics
- Steve Zelditch
- Jean Bourgain
- P. P. Varj'u
- Larry Guth
- Massimiliano Berti
- Christopher D. Sogge
- Peter Sarnak
- Alex Kontorovich
Citations in the corpus
- EIGENFUNCTIONS AND NODAL SETS (2012, background): “recent paper of J. Jung shows that many natural curves in the hyperbolic plane are ‘good’ [JJ]. 8.3. Application to Pleijel’s conjecture. We also note an interesting application due to I. Polterovich [Po] of Theorem 8.1 to an old conjecture of A. Pleijel regarding Courant’s nodal domain theorem, whi”
- On Pleijel's Nodal Domain Theorem (2013, methodology): “While it was already pointed out in [11] that Pleijel’s inequality is not sharp, the purpose of this note is to carry out a refinement of Pleijel’s argument that leads to an explicit small improvement of (1).”