34 citations · 150 across the 29 of their papers we have counts for
9 papers · 1 filter
The Semiclassical Resolvent on Conic Manifolds and Application to Schrödinger Equations
Xi Chen
In this article, we shall construct the resolvent of Laplacian at high energies near the spectrum on non-product conic manifolds with a single cone tip. Microlocally, the resolvent…
Inverse problem for the Yang-Mills equations
Xi Chen, Matti Lassas, Lauri Oksanen +1
We show that a connection can be recovered up to gauge from source-to-solution type data associated with the Yang-Mills equations in the four dimensional Minkowski space. Our proof…
Detection of Hermitian connections in wave equations with cubic non-linearity
Xi Chen, Matti Lassas, Lauri Oksanen +1
We consider the geometric non-linear inverse problem of recovering a Hermitian connection from the source-to-solution map of the cubic wave equation , wh…
The Sobolev Inequalities on Real Hyperbolic Spaces and Eigenvalue Bounds for Schrödinger Operators with Complex Potentials
Xi Chen
In this paper, we prove the uniform estimates for the resolvent as a map from to on real hyperbolic space where $α\in \mathbb{C}\setminu…
The Heat Kernel on Asymptotically Hyperbolic Manifolds
Xi Chen, Andrew Hassell
Upper and lower bounds on the heat kernel on complete Riemannian manifolds were obtained in a series of pioneering works due to Cheng-Li-Yau, Cheeger-Yau and Li-Yau. However, these…
Stein-Tomas Restriction Theorem via Spectral Measure on Metric Measure Spaces
Xi Chen
The Stein-Tomas restriction theorem on Euclidean space says one can meaningfully restrict to the unit sphere of provided with $1…