Skip to main content

Integral-Geometric Formulas

  • Chapter
  • First Online:
Lectures on Convex Geometry

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 286))

  • 3320 Accesses

Abstract

In this chapter, we discuss various integral formulas for intrinsic volumes, which are based on projections, sections or sums of convex bodies. We shall also discuss some applications of a stereological nature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 69.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Alesker, S., Fu, J.H.G.: In: Gallego, E., Solanes, G. (eds.) Integral Geometry and Valuations. Advanced Courses in Mathematics. CRM Barcelona, viii+112 pp. Birkhäuser/Springer, Basel (2014). Lectures from the Advanced Course on Integral Geometry and Valuation Theory held at the Centre de Recerca Matemàtica (CRM), Barcelona, 6–10 September 2010

    Google Scholar 

  2. Bernig, A.: Algebraic integral geometry. In: Global Differential Geometry. Springer Proceedings in Mathematics, vol. 17, pp. 107–145. Springer, Berlin (2012)

    Google Scholar 

  3. Cohn, D.L.: Measure Theory. Birkhäuser, Boston (1997)

    Google Scholar 

  4. Jensen, E.B.V., Kiderlen, M.: Tensor Valuations and Their Applications in Stochastic Geometry and Imaging. Lecture Notes in Mathematics, vol. 2177. Springer, Cham (2017)

    Google Scholar 

  5. Nachbin, L.: The Haar Integral. Van Nostrand, Princeton (1965)

    MATH  Google Scholar 

  6. Schneider, R.: Convex Bodies: The Brunn-Minkowski Theory, 2nd expanded edn. Cambridge University Press, Cambridge (2014)

    Google Scholar 

  7. Schneider, R., Weil, W.: Integralgeometrie. Teubner, Stuttgart (1992)

    Book  Google Scholar 

  8. Schneider, R., Weil, W.: Stochastische Geometrie. Teubner, Stuttgart (2000)

    Book  Google Scholar 

  9. Schneider, R., Weil, W.: Stochastic and Integral Geometry. Springer, Berlin (2008)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Daniel Hug .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Hug, D., Weil, W. (2020). Integral-Geometric Formulas. In: Lectures on Convex Geometry. Graduate Texts in Mathematics, vol 286. Springer, Cham. https://doi.org/10.1007/978-3-030-50180-8_5

Download citation

Publish with us

Policies and ethics