Strichartz estimates for the Schrödinger equation on Zoll manifolds

Fuente: arXiv
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Main Authors: Huang, Xiaoqi, Sogge, Christopher D.
Format: Preprint
Published: 2025
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author Huang, Xiaoqi
Sogge, Christopher D.
author_facet Huang, Xiaoqi
Sogge, Christopher D.
contents We obtain optimal space-time estimates in $L^q_{t,x}$ spaces for all $q\ge 2$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_00884
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Strichartz estimates for the Schrödinger equation on Zoll manifolds
Huang, Xiaoqi
Sogge, Christopher D.
Analysis of PDEs
Classical Analysis and ODEs
Differential Geometry
We obtain optimal space-time estimates in $L^q_{t,x}$ spaces for all $q\ge 2$ 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.
title Strichartz estimates for the Schrödinger equation on Zoll manifolds
topic Analysis of PDEs
Classical Analysis and ODEs
Differential Geometry
url https://arxiv.org/abs/2505.00884