MCS-MP Seminar: Roméo Leylekian

Speaker: Roméo Leylekian

Title: Neumann's nodal line

Abstract: We show the existence of planar domains with one hole for which the first non-trivial Neumann eigenfunction has a closed nodal line fully contained inside the domain. This is optimal and shows that Pleijel’s result on the non-closure of the nodal line does not hold aside from simply-connected domains. Part of the proof is based on the study of metric graphs and graph-like domains.

This work was performed in collaboration with Pedro Freitas.