17 citations · 50 across the 20 of their papers we have counts for
26 papers
Recovery of coefficients in a Schrödinger system with nonlinear coupling
Pranav Arrepu, Hanming Zhou
We consider the inverse problem of recovering time-dependent coefficients in a system of Schrödinger equations with coupled nonlinear terms. We first address the well-posedness of…
Conformal boundary rigidity for simple Finsler metrics
Kelvin Lam, Hanming Zhou
In this paper we prove that simple Finsler manifolds are conformally stable. Given a simple Finsler manifold and a class of conformal factors, we characterize the singularity of th…
The BGK model with in-flow boundary condition: forward and inverse problems
Ru-Yu Lai, Hanming Zhou
We study the Bhatnagar-Gross-Krook (BGK) equation in a bounded domain with in-flow boundary condition. The BGK model is a simple relaxation of the Boltzmann equation through replac…
The linearized minimal surfaces problem
Haim Grebnev, Plamen Stefanov, Gunther Uhlmann +1
We characterize the kernel of the linearization of the minimal surface problem about the Euclidean metric in a bounded smooth domain , , with the b…
Stable Determination of Coefficients in Nonlinear Dynamical Schrödinger Equations by Carleman Estimates
Pranav Arrepu, Hanming Zhou
We consider the inverse problem of recovering stationary coefficients in a class of dynamical Schrödinger equations with locally analytic nonlinear terms. Upon treating the well-po…
Inverse problems for time-dependent nonlinear transport equations
Ru-Yu Lai, Hanming Zhou
In this work, we investigate inverse problems of recovering the time-dependent coefficient in the nonlinear transport equation in both cases: two-dimensional Riemannian manifolds a…
Stability and Statistical Inversion of Travel time Tomography
Ashwin Tarikere, Hanming Zhou
In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the length…
On the Identifiablility of Nonlocal Interaction Kernels in First-Order Systems of Interacting Particles on Riemannian Manifolds
Sui Tang, Malik Tuerkoen, Hanming Zhou
In this paper, we tackle a critical issue in nonparametric inference for systems of interacting particles on Riemannian manifolds: the identifiability of the interaction functions.…
Recovery of coefficients in semilinear transport equations
Ru-Yu Lai, Gunther Uhlmann, Hanming Zhou
We consider the inverse problem for time-dependent semilinear transport equations. We show that time-independent coefficients of both the linear (absorption or scattering coefficie…
Single pixel X-ray transform and related inverse problems
Ru-Yu Lai, Gunther Uhlmann, Jian Zhai +1
In this paper, we analyze the nonlinear single pixel X-ray transform and study the reconstruction of from the measurement . Different from the well-known X-ray transfor…
Inverse source problems in transport equations with external forces
Ru-Yu Lai, Hanming Zhou
This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for gene…
Global determination for an inverse problem from the vortex dynamics
Ru-Yu Lai, Hanming Zhou
We consider the problem of reconstructing a background potential from the dynamical behavior of vortex dipole. We prove that under suitable conditions, one can uniquely reconstruct…
Travel time tomography in stationary spacetimes
Gunther Uhlmann, Yang Yang, Hanming Zhou
In this paper, we consider the boundary rigidity problem on a cylindrical domain in , , equipped with a stationary (time-invariant) Lorentzian metric. We…
Lens rigidity for a particle in a Yang-Mills field
Gabriel P. Paternain, Gunther Uhlmann, Hanming Zhou
We consider the motion of a classical colored spinless particle under the influence of an external Yang-Mills potential on a compact manifold with boundary of dimension $\geq 3…
Reconstruction of a compact Riemannian manifold from the scattering data of internal sources
Matti Lassas, Teemu Saksala, Hanming Zhou
Given a smooth non-trapping compact manifold with strictly con- vex boundary, we consider an inverse problem of reconstructing the manifold from the scattering data initiated from…
Generic injectivity and stability of inverse problems for connections
Hanming Zhou
We consider the nonlinear problem of determining a connection and a Higgs field from the corresponding parallel transport along geodesics on a Riemannian manifold with boundary, in…
The local magnetic ray transform of tensor fields
Hanming Zhou
In this paper we study the local magnetic ray transform of symmetric tensor fields up to rank two on a Riemannian manifold of dimension with boundary. In particular, we co…
Lens rigidity with partial data in the presence of a magnetic field
Hanming Zhou
In this paper we consider the lens rigidity problem with partial data for conformal metrics in the presence of a magnetic field on a compact manifold of dimension with bou…
The geodesic X-ray transform with matrix weights
Gabriel P. Paternain, Mikko Salo, Gunther Uhlmann +1
Consider a compact Riemannian manifold of dimension with strictly convex boundary, such that the manifold admits a strictly convex function. We show that the attenuated ra…
Journey to the Center of the Earth
Gunther Uhlmann, Hanming Zhou
We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves go…
Invariant distributions and the geodesic ray transform
Gabriel P. Paternain, Hanming Zhou
We establish an equivalence principle between the solenoidal injectivity of the geodesic ray transform acting on symmetric -tensors and the existence of invariant distributions…
Injectivity and stability for a generic class of generalized Radon transforms
Andrew Homan, Hanming Zhou
Let (M,g) be an analytic, compact, Riemannian manifold with boundary, of dimension n >= 2. We study a class of generalized Radon transforms, integrating over a family of hypersurfa…
Invariant distributions and tensor tomography for Gaussian thermostats
Yernat M. Assylbekov, Hanming Zhou
In this paper we consider the Gaussian thermostat ray transform on both closed Riemannian surfaces and compact Riemannian surfaces with boundary. We establish certain results on th…
An Inverse Kinematic Problem with Internal Sources
Leonid Pestov, Gunther Uhlmann, Hanming Zhou
Given a bounded domain in with a conformally Euclidean metric , in this paper we consider the inverse problem of recovering a semigeodesic neighborhoo…