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Global Differential Geometry pp 107–145Cite as

Algebraic Integral Geometry

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Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 17))

Abstract

A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.

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Acknowledgements

I was happy to profit from many discussions with and talks by Semyon Alesker and Joseph Fu on algebraic integral geometry. The present text is strongly influenced by their ideas and I am grateful to them. The terms Algebraic integral geometryand Fundamental theorem of algebraic integral geometrywere invented by Fu. I also thank Gautier Berck, Franz Schuster and Christoph Thäle for numerous useful remarks on this text.

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Authors and Affiliations

  1. Institut für Mathematik, Goethe-Universität Frankfurt, Robert-Mayer-Str. 10, 60054, Frankfurt, Germany

    Andreas Bernig

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  1. Andreas Bernig
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Correspondence to Andreas Bernig .

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Editors and Affiliations

  1. Inst. Mathematik, Universität Potsdam, Potsdam, Brandenburg, Germany

    Christian Bär

  2. , Mathematisches Institut, Universität Münster, Einsteinstraße 62, Münster, 48149, Germany

    Joachim Lohkamp

  3. , Fakultät für Mathematik und Informatik, Universität Leipzig, Johannisgasse 26, Leipzig, 04103, Sachsen, Germany

    Matthias Schwarz

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Bernig, A. (2012). Algebraic Integral Geometry. In: Bär, C., Lohkamp, J., Schwarz, M. (eds) Global Differential Geometry. Springer Proceedings in Mathematics, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22842-1_5

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