28 citations · 154 across the 37 of their papers we have counts for
25 papers · 1 filter
The Calderón problem for near-Euclidean metrics
Gunther Uhlmann, Yiran Wang
In this article, we consider the anisotropic Calderón problem of determining the potential from boundary measurements of the time-independent Schrödinger equation on compact Rieman…
The partial data Calderón problem in dimension three
Gunther Uhlmann, Yiran Wang
We consider an inverse boundary value problem for the time-independent Schrödinger equation in dimension three. We prove that the local Dirichlet-to-Neumann map defined near a boun…
Inverse source problem for the Boltzmann equation in cosmology
Yiran Wang
We study the inverse problem of recovering primordial perturbations from anisotropies of Cosmic Microwave Background (CMB) using the kinetic model. Mathematically, the problem in c…
Recovery of black hole mass from a single quasinormal mode
Gunther Uhlmann, Yiran Wang
We study the determination of the mass of a de Sitter-Schwarzschild black hole from one quasinormal mode. We prove a local uniqueness result with a Hölder type stability estimate.
Some integral geometry problems for wave equations
Yiran Wang
We consider the Cauchy problem and the source problem for normally hyperbolic operators on the Minkowski spacetime, and study the determination of solutions from their integrals al…
Microlocal analysis of the light ray transform on globally hyperbolic Lorentzian manifolds
Yiran Wang
For the light ray transform on globally hyperbolic Lorentzian manifolds of dimension acting on compactly supported distributions, we show that the Schwartz kernel of t…
The anisotropic Calderón problem for high fixed frequency
Gunther Uhlmann, Yiran Wang
We consider Schrödinger operators at a fixed high frequency on simply connected compact Riemannian manifolds with non-positive sectional curvatures and smooth strictly convex bound…
Inverse Scattering for Critical Semilinear Wave Equations
Antônio Sá Barreto, Gunther Uhlmann, Yiran Wang
We show that the scattering operator for defocusing energy critical semilinear wave equations \square u+f(u)=0, with f C-infinity and f ~ u^5, in three space dimensions, determines…
Sharp resolvent estimates on non-positively curved asymptotically hyperbolic manifolds
Yiran Wang
We study the high energy estimate for the resolvent of the Laplacian on non-trapping asymptotically hyperbolic manifolds (AHM). In the literature, polynomial bound of the fo…
On the light ray transform of wave equation solutions
András Vasy, Yiran Wang
We study the light ray transform on Minkowski space-time and its small metric perturbations acting on scalar functions which are solutions to wave equations. We show that the light…
Convolutional neural networks in phase space and inverse problems
Gunther Uhlmann, Yiran Wang
We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of pr…
Singularities generated by the triple interaction of semilinear conormal waves
Antônio Sá Barreto, Yiran Wang
We study the local propagation of conormal singularities for solutions of semilinear wave equations , where is a polynomial of degree in $…
Determination of space-time structures from gravitational perturbations
Gunther Uhlmann, Yiran Wang
We study inverse problems for the Einstein equations with source fields in a general form. Under a microlocal linearization stability condition, we show that by generating small gr…
Nonlinear interaction of waves in elastodynamics and an inverse problem
Maarten de Hoop, Gunther Uhlmann, Yiran Wang
We consider nonlinear elastic wave equations generalizing Gol'dberg's five constants model. We analyze the nonlinear interaction of two distorted plane waves and characterize the p…
Quantitative analysis of metal artifacts in X-ray tomography
Benjamin Palacios, Gunther Uhlmann, Yiran Wang
In X-ray CT scan with metallic objects, it is known that direct application of the filtered back-projection (FBP) formula leads to streaking artifacts in the reconstruction. These…
Nonlinear responses from the interaction of two progressing waves at an interface
Maarten de Hoop, Gunther Uhlmann, Yiran Wang
For scalar semilinear wave equations, we analyze the interaction of two (distorted) plane waves at an interface between media of different nonlinear properties. We show that new wa…
Determination of vacuum space-times from the Einstein-Maxwell equations
Matti Lassas, Gunther Uhlmann, Yiran Wang
We study inverse problems for the Einstein-Maxwell equations. We prove that it is possible to generate gravitational waves from the nonlinear interactions of electromagnetic waves.…
Parametrices for the light ray transform on Minkowski spacetime
Yiran Wang
We consider restricted light ray transforms arising from an inverse problem of finding cosmic strings. We construct a relative left parametrix for the transform on two tensors, whi…
Inverse problems for quadratic derivative nonlinear wave equations
Yiran Wang, Ting Zhou
For semilinear wave equations on Lorentzian manifolds with quadratic derivative non-linear terms, we study the inverse problem of determining the background Lorentzian metric. Unde…
Reducing Streaking Artifacts in Quantitative Susceptibility Mapping
Benjamin Palacios, Gunther Uhlmann, Yiran Wang
It is well-known that reconstruction algorithms in quantitative susceptibility mapping often contain streaking artifacts. In [1], the cause of the artifacts is identified as propag…
The scattering operator on asymptotically hyperbolic manifolds
Antônio Sá Barreto, Yiran Wang
We obtain a formula for the Schwartz kernel of the scattering operator in terms of the Schwartz kernel of the fundamental solution of the wave operator on asymptotically hyperbolic…
Inverse problems for semilinear wave equations on Lorentzian manifolds
Matti Lassas, Gunther Uhlmann, Yiran Wang
We consider inverse problems in space-time , a -dimensional Lorentzian manifold. For semilinear wave equations , where denotes the…
High Energy Resolvent Estimates on Conformally Compact Manifolds with Variable Curvature at Infinity
Antonio Sa Barreto, Yiran Wang
We construct a semiclassical parametrix for the resolvent of the Laplacian acing on functions on non-trapping conformally compact manifolds with variable sectional curvature at inf…
Resolvent and Radiation Fields on Non-trapping Asymptotically Hyperbolic Manifolds
Yiran Wang
We construct a semi-classical parametrix for the Laplacian on non-trapping asymptotically hyperbolic manifolds, which generalizes the construction of Melrose, Sa Barreto and Vasy.…