Seminar: Sharp Spectral-Cluster Restriction Bounds for Orthonormal Systems

Seminar| Institute of Mathematical Sciences

Time:Wednesday, July 9th, 2025,10:00-11:00

Abstract: For a smooth k-dimensional submanifold Σ of a d-dimensional compact Riemannian manifold (M,g), we extend the L^p(Σ) restriction bounds of Burq, Gérard, and Tzvetkov [Duke, 2007] from individual Laplace–Beltrami eigenfunctions to systems of L^2(M)-orthonormal functions. Our bounds are essentially optimal for every triple (k,d,p) with p ≥ 2, except possibly when d ≥ 3, k = d−1, and 2 ≤ p < 4. This work is inspired by Frank and Sabin [Adv. Math, 2017], who established analogous L^p(M) bounds for L^2(M)-orthonormal systems.