Nodal sets of eigenfunctions of the Laplacian and optimal transport in singular spaces.

par Sara Farinelli

lundi 5 juin 2023, 10:00 → 11:00 Europe/Paris

Bâtiment Buffon, salle RH04A (Université Paris-Cité (campus Grands Moulins))

Upper and lower bounds of the Hausdorff measure of nodal sets of Laplace eigenfunctions have been largely studied in the context of smooth Riemannian manifolds, while very little is known in the context of possibly singular spaces. We investigate this problem in the setting of metric measure spaces satisfying a notion of curvature bound, using optimal transport. In particular we focus on estimates of the Wasserstein distance between the positive part and the negative part of an eigenfunction.