Abstract : Let D be a bounded domain in R^n with C^1 boundary and let u be a Dirichlet Laplace eigenfunction in D with eigenvalue λ. We show that the (n − 1)-dimensional Hausdorff measure of the zero set of u does not exceed C√λ. The opposite estimate follows from the work of Donnelly and Fefferman. The talk is based on a joint work with A. Logunov, N. Nadirashvili, and F. Nazarov..
https://univ-cotedazur.zoom.us/j/89934300280?pwd=SzRTOVZZV1ZOY1JBeGU4T2NndkV2UT09 Meeting ID: 899 3430 0280 Acces code: 799851.