Qiuye Jia

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20242026

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math.AP2026

Determining metrics from the scattering map of the time-dependent Schrödinger equation

Qiuye Jia

For a time dependent Schrödinger 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 Schrödinger operator $D_{t} + Δ_{g}$ with metric and potential perturbation that are compactly supported in spacetime $R^{n + 1}$ . Here $D_{t} = - i \partial_{t}$ and $Δ_g…

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 $X = (0, \infty) \times S_{σ}^{1}$ . The operator $S_{λ}^{δ} (Δ_{X})$ is bounded on $L^{p} (X)$ fo…

math.AP2025

Decay and Strichartz estimates for critical electromagnetic wave equations on conic manifolds

Qiuye Jia, Junyong Zhang

We establish the decay and Strichartz estimates for the wave equation with large scaling-critical electromagnetic potentials on a conical singular space $(X, g)$ with dimension $n\g…

math.AP2024

Strichartz estimates for the Schrödinger equation in high dimensional critical electromagnetic fields

Qiuye Jia, Junyong Zhang

We prove Strichartz estimates for the Schrödinger equation with scaling-critical electromagnetic potentials in dimensions $n \geq 3$ . The decay assumption on the magnetic potentials…