C1 Book
Geometric Inverse Problems : With Emphasis on Two Dimensions (2023)

Paternain, G. P., Salo, M., & Uhlmann, G. (2023). Geometric Inverse Problems : With Emphasis on Two Dimensions. Cambridge University Press. Cambridge Studies in Advanced Mathematics, 204. https://doi.org/10.1017/9781009039901

JYU authors or editors

Publication details

All authors or editors: Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther

ISBN: 978-1-316-51087-2

eISBN: 978-1-009-03990-1

Journal or series: Cambridge Studies in Advanced Mathematics

ISSN: 0950-6330

Publication year: 2023

Publication date: 05/01/2023

Number in series: 204

Number of pages in the book: 344

Publisher: Cambridge University Press

Place of Publication: Cambridge

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1017/9781009039901

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/85367

Abstract

This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary rigidity, tensor tomography, attenuated X-ray transforms and the Calderón problem. The presentation is self-contained and begins with the Radon transform and radial sound speeds as motivating examples. The required geometric background is developed in detail in the context of simple manifolds with boundary. An in-depth analysis of various geodesic X-ray transforms is carried out together with related uniqueness, stability, reconstruction and range characterization results. Highlights include a proof of boundary rigidity for simple surfaces as well as scattering rigidity for connections. The concluding chapter discusses current open problems and related topics. The numerous exercises and examples make this book an excellent self-study resource or text for a one-semester course or seminar.

Keywords: mathematics; geometry; inverse problems; topology; geodesy

Free keywords: mathematics; abstract analysis; geometry and topology

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2023

Preliminary JUFO rating: 1