Strichartz estimates for orthonormal systems on compact manifolds: the non-sharp region
Abstract
We establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the non-sharp admissible region of exponents, covering wave, Klein-Gordon, and fractional Schr\"odinger equations. Our approach combines the result of Wang-Zhang-Zhang wang2025strichartz on the sharp admissible line with a Lieb-Sobolev inequality derived from a recent Cwikel estimate due to Sukochev-Yang-Zanin sukochev2025singular, along with an alternative globalization method based on localized weak Lorentz estimates. Our results extend the Euclidean results of Bez-Hong-Lee-Nakamura-Sawano bez2019strichartz and Bez-Lee-Nakamura bez2021strichartz, as well as the classical single-function estimates on manifolds due to Kapitanski kapitanski1989some, Burq-G\'erard-Tzvetkov MR2058384, and Dinh dinh2016strichartz.
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