Séminaires : Séminaire d'Analyse Fonctionnelle

Equipe(s) : af,
Responsables :E. Abakoumov - A.Eskenazis - D. Cordero-Erausquin - M. Fathi - O. Guédon - B. Maurey
Email des responsables :
Salle : salle 13 - couloir 15-16 - 4ème étage
Adresse :Campus Pierre et Marie Curie
Le Jeudi à 10h30 -  IMJ-PRG - 4 place Jussieu - 75005 PARIS

Orateur(s) Alexander Logunov - IAS, Princeton,
Titre Zero sets of Laplace eigenfunctions
Horaire10:00 à 13:35
RésumeNadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite area. Nadirashvili's conjecture is true and we will discuss its applications to the Yau conjecture on zero sets of Laplace eigenfunctions. Both conjectures can be treated as an attempt to control the zero set of a solution of elliptic PDE in terms of growth of the solution. For holomorhpic functions such kind of control is possible only from one side: there is a plenty of holomorphic functions that have no zeros. While for a real-valued harmonic function on a plane the length of the zero set can be estimated (locally) from above and below in terms of growth of the harmonic function. We will discuss the notion of frequency, its properties and applications to the zero sets of harmonic functions in the higher dimensional case.
Sallesalle 13 - couloir 15-16 - 4ème étage
AdresseCampus Pierre et Marie Curie