Leo Tzou

Identification of a Connection from Cauchy Data on a Riemann Surface with Boundary

We consider a connection

Calderón inverse problem with partial data on Riemann surfaces

{\nabla^X}

A variational principle for gradient flows

on a complex line bundle over a Riemann surface with boundary M0, with connection 1-form X. We show that the Cauchy data space of the connection Laplacian (also called magnetic Laplacian)

Inverse problems with partial data for a Dirac system: A Carleman estimate approach

{L := \nabla^X{^*\nabla^X} + q}

Inverse Scattering at Fixed Energy on Surfaces with Euclidean Ends

, with q a complex-valued potential, uniquely determines the connection up to gauge isomorphism, and the potential q.

Partial data inverse problems for the Hodge Laplacian

We prove a fixed frequency inverse scattering result for the magnetic Schrödinger operator (or connection Laplacian) on surfaces with Euclidean ends. We show that, under suitable decaying conditions, the scattering matrix for the operator determines both the gauge class of the connection and the zeroth order potential.