On local smoothing estimates for wave equations

TL;DR

This paper establishes sharp local smoothing estimates for wave equations on compact Riemannian manifolds and Euclidean spaces, with improvements in even dimensions through Fourier integral operators.

Contribution

It introduces new sharp local smoothing estimates for wave equations on manifolds and Euclidean spaces, especially enhancing results in even dimensions.

Findings

Sharp local smoothing estimates for wave equations on compact manifolds

Improved estimates in even-dimensional Euclidean spaces

Use of Fourier integral operators to derive smoothing estimates

Abstract

We prove sharp local smoothing estimates for wave equations on compact Riemannian manifolds in $n+1$ dimensions for odd $n$ and obtain improved estimates in even dimensions. This is achieved by deriving local smoothing estimates for certain Fourier integral operators. We also obtain improved local smoothing estimates for wave equations in Euclidean spaces.