This research demonstrates optimal space-time estimates for the Schrödinger equation on Zoll manifolds, suggesting connections to oscillatory integrals.
We obtain optimal space-time estimates in Lqt,x spaces for all q≥ 2 for solutions to the Schr\"odinger equation on Zoll manifolds, including, in particular, the standard round sphere Sᵈ. 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.
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Huang et al. (2025) studied this question.
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