6 papers
Global recovery of Lorentzian principal geometry from the hyperbolic Dirichlet-to-Neumann map
Lu Chen, Yan Jiang, Hongyu Liu +1
We prove that the full Dirichlet-to-Neumann map on a finite time interval globally determines the Lorentzian metric \(\mathbf G_{g,c}=-c(x,t)^2\mathrm{d}t^2+g(x)\) encoded by the p…
Boundary Spectral Inequalities from Measurable Sets on manifolds and their applications
Lu Chen, Haolin Liu, Hongyu Liu
Let be a compact connected Riemannian manifold with nonempty boundary and a uniformly elliptic Lipschitz metric. We establish quantitative boundary…
Quasianalyticity and geometric rigidity in anisotropic Calderón's problem
Lu Chen, Yan Jiang, Hongyu Liu +1
The anisotropic Calderón problem of determining a smooth Riemannian metric from boundary measurements, up to a boundary-fixing diffeomorphism, remains open in dimensions ~\c…
Inverse Scattering from Conformal Infinity for Totally Geodesic Defects in Hyperbolic Space
Lu Chen, Hongyu Liu, Longyue Tao
We study inverse scattering from conformal infinity for impenetrable topological defects whose interaction surfaces are totally geodesic in hyperbolic space \(\mathbb H^n\), \(n \g…
Determining evolutionary equations from a single passive boundary observation
Lu Chen, Yan Jiang, Hongyu Liu +2
We study inverse boundary problems for evolutionary PDEs using only a single passive boundary observation, where data from an unknown internal source propagate through an unknown m…
The Sommerfeld-Rellich Framework for Scattering on Hyperbolic Space: Far-Field Patterns and Inverse Problems
Lu Chen, Hongyu Liu
This paper establishes a complete time-harmonic scattering theory for hyperbolic space, formulating it within the classical Sommerfeld-Rellich paradigm centered on far-field patter…