Rigidity in the Lorentzian Calderón problemOberseminar Analysis

by Prof. Mikko Salo (University of Jyväskylä)

Monday Feb 17, 2025, 2:15 AM → 4:00 AM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

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).