Qiuye Jia

activity

20242026

collaborators

10 papers

math.AP2026

Determining potentials from the scattering map of the time-dependent SchrÃ¶dinger equation

Qiuye Jia

For a time dependent SchrÃ¶dinger equation, the scattering map is the map sending the asymptotic profile of a solution as $t \to - \infty$ to its asymptotic profile as $t \to + \infty$ .…

math.AP2026

The effect of geometric focusing on dispersive estimates for the Schrödinger and wave equations

Qiuye Jia, Junyong Zhang

We classify the long-time decay rate in dispersive estimates for the Schrödinger and wave equations on non-trapping asymptotically conic manifolds and exact metric cones in terms o…

math.AP2026

Determining metrics from the scattering map of the time-dependent SchrÃ¶dinger equation

Qiuye Jia

For a time dependent SchrÃ¶dinger equation, the scattering map is the map sending the asymptotic profile of solution as $t \to - \infty$ to its asymptotic profile as $t \to + \infty$ . In…

math.AP2026

Lecture notes on non-elliptic Fredholm theory

Andrew Hassell, Qiuye Jia, Ethan Sussman

These are lecture notes from the Austral Winter School on Microlocal Analysis and Non-elliptic Fredholm Theory, held at the Australian National University, Canberra, June 30 -- Jul…

math.AP2026

The scattering map for the Schrodinger operator on curved spaces

Andrew Hassell, Qiuye Jia

Let $P$ be a SchrÃ¶dinger operator $D_{t} + I^_{g}$ with metric and potential perturbation that are compactly supported in spacetime $R^{n + 1}$ . Here $D_{t} = - i \partial_{t}$ and $Î…

math.AP2025

Bochner-Riesz means on a conical singular manifold

Qiuye Jia, Junyong Zhang, Jiqiang Zheng

We prove a sharp $L^{p}$ -boundedness criterion for Bochner-Riesz multipliers on flat cones $X = (0, \infty) \times S_{I ¨} ^{1}$ . The operator $S_{I^} »^{I^} ´ (I^_{X})$ is bounded on $L^p(X)…