Skip to main content Accessibility help
×
  1. Home
  2. Books
  3. Geometric Inverse Problems
  • Cited by 32
      • Show more authors
      • You may already have access via personal or institutional login
    • Select format
    • Publisher:
      Cambridge University Press
      Publication date:
      January 2023
      January 2023
      ISBN:
      9781009039901
      9781316510872
      DOI:
      https://doi.org/10.1017/9781009039901
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.71kg, 370 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Geometry and Topology
      Series:
      Cambridge Studies in Advanced Mathematics (204)
    You may already have access via personal or institutional login
    • Selected: Digital
    Add to cart View cart Buy from Cambridge.org
    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Geometry and Topology
    Series:
    Cambridge Studies in Advanced Mathematics (204)
    Information

    Book description

    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.

    Reviews

    ‘This monograph gives a beautiful introduction to Geometric inverse problems, largely in dimension two, by three of the most prominent contributors to the field. The Geometric problems are interesting as pure mathematics, but they also arise from applications to tomography, such as the Calderon problem of determining (M, g) from its Dirichlet-to-Neumann map. Roughly speaking, the underlying physics problem is to determine electrical properties of a medium by making voltage and current measurements on the boundary. Techniques of microlocal analysis relate such PDE boundary inverse problems to geometric inverse problems. These inverse problems furnish problems of great interest in PDE and in geometry in a rather concrete setting, and are masterfully conveyed by the authors. The level is appropriate for a graduate class in mathematics but is also an excellent entrée into the field for research mathematicians.’

    Steve Zelditch - Northwestern University

    Refine List

    Actions for selected content:

    Select all | Deselect all
    • View selected items
    • Export citations
    • Download PDF (zip)
    • Save to Kindle
    • Save to Dropbox
    • Save to Google Drive

    Save Search

    You can save your searches here and later view and run them again in "My saved searches".

    Please provide a title, maximum of 40 characters.
    Cancel
    ×

    Contents

    Contents
    References

    Metrics

    Altmetric attention score

    Full text views

    Total number of HTML views: 0
    Total number of PDF views: 0 *
    Loading metrics...

    Book summary page views

    Total views: 0 *
    Loading metrics...

    * Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

    Usage data cannot currently be displayed.

    Accessibility standard: Unknown

    Why this information is here

    This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

    Accessibility Information

    Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.