Strichartz estimates for the Schrödinger equation on Zoll manifolds
Abstract
We obtain optimal space-time estimates in L q t,x spaces for all q ≥ 2 for solutions to the Schrödinger equation on Zoll manifolds, including, in particular, the standard round sphere S d .The proof relies on the arithmetic properties of the spectrum of the Laplacian on Zoll manifolds, as well as bilinear oscillatory integral estimates, which allow us to relate the problem to Strichartz estimate on one-dimensional tori.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Mathematical Analysis and Transform Methods
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Beijing Journal of Pure and Applied Mathematics
- Publisher
- International Press of Boston
- Volume
- 3
- Issue
- 1
- Pages
- 35–65
- Publication date
- 1 January 2026
- Language
- EN