On geometric inverse problems and microlocal analysis

Abstract

This work gives an expository account of certain applications of microlocal analysis in three geometric inverse problems. We will discuss the geodesic X-ray transform inverse problem, the Gelfand problem for the wave equation on a Riemannian manifold, and the Calderón problem for the Laplace equation on a Riemannian manifold.

arXiv comment60 pages. This material is based on lecture notes for two online minicourses, one organized at DTU, Copenhagen, in January 2021 and another at CRM, Montreal, in August 2021. This work follows earlier lecture notes (arXiv:1908.03041, published in https://doi.org/10.3390/math8071184) and extends the results from Euclidean to Riemannian background geometry. arXiv admin note: text overlap with arXiv:1908.03041