Title: Strichartz estimates for the Schrödinger equation on Zoll manifolds Show Chinese title

Title: Zoll流形上薛定谔方程的Strichartz估计

Abstract: We obtain optimal space-time estimates in $L^q_{t,x}$ spaces for all $q\ge 2$ for solutions to the Schr\"odinger 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. Show Chinese abstract

Abstract: 我们在Zoll流形上获得了Schrödinger方程解在所有$q\ge 2$空间中的最优时空估计，这些估计是在$L^q_{t,x}$空间中得到的，特别包括标准的单位球$S^d$。 证明依赖于Zoll流形上Laplacian谱的算术性质，以及双线性振荡积分估计，这使我们能够将问题与一维环面的Strichartz估计联系起来。