UAM-ICMAT EDP Seminar
A Calderón problem for Beltrami fields
Speaker: Carlos Valero (ICMAT)Date: Friday, 31 January 2025 - 12:15Place: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Abstract:
We define an analogue of the Dirichlet-to-Neumann map for Beltrami fields, which are eigenvectors of the curl operator on a 3-dimensional Riemannian manifold with boundary. This map sends the normal component of a Beltrami field to its tangential component on the boundary. We first show that this normal-to-tangential map is a pseudodifferential operator of order 0 whose full symbol determines the Taylor series of the metric at the boundary. Then, by adapting an approach based on Green’s functions used to solve the classical Calderón problem in the case of analytic data, we go on to show that a real-analytic simply connected 3-manifold can be recovered up to isometry from its normal-to-tangential map
