Rigidity in the Lorentzian Calderón problem (joint w/ IP seminar)

The inverse problem of Calderón, in its geometric formulation, asks if
a Riemannian metric in a domain is determined up to isometry by
boundary measurements of harmonic functions. Physically this
corresponds to determining a matrix electrical conductivity function
from voltage and current measurements on the boundary. This problem is
open in general.

In this talk we will discuss the hyperbolic analogue of the Calderón
problem for the (Lorentzian) wave equation. We will show a rigidity
result stating that any globally hyperbolic Lorentzian metric can be
distinguished from the Minkowski metric. The result is valid for
formally determined data and the method is based on distorted plane
waves and geometric, topological and unique continuation arguments.
This is joint work with L. Oksanen (Helsinki) and Rakesh (Delaware).