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Analytic Aspects of Convexity pp 1–17Cite as

Dual Curvature Measures in Hermitian Integral Geometry

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Part of the book series: Springer INdAM Series ((SINDAMS,volume 25))

Abstract

The local kinematic formulas on complex space forms induce the structure of a commutative algebra on the space CurvU(n)∗ of dual unitarily invariant curvature measures. Building on the recent results from integral geometry in complex space forms, we describe this algebra structure explicitly as a polynomial algebra. This is a short way to encode all local kinematic formulas. We then characterize the invariant valuations on complex space forms leaving the space of invariant angular curvature measures fixed.

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References

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Acknowledgements

Andreas Bernig was supported by DFG grant BE 2484/5-2. Joseph H.G. Fu was supported by NSF grant DMS-1406252. Gil Solanes is a Serra Húnter Fellow and was supported by FEDER-MINECO grant MTM2015-66165-P.

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Authors and Affiliations

  1. Institut für Mathematik, Goethe-Universität Frankfurt, Frankfurt, Germany

    Andreas Bernig

  2. Department of Mathematics, University of Georgia, Athens, GA, USA

    Joseph H. G. Fu

  3. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Spain

    Gil Solanes

Authors
  1. Andreas Bernig
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  2. Joseph H. G. Fu
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  3. Gil Solanes
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Corresponding author

Correspondence to Andreas Bernig .

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Editors and Affiliations

  1. Dept. of Mathematics and Computer Science “U. Dini”, University of Florence, Florence, Italy

    Gabriele Bianchi

  2. Dept. of Mathematics and Computer Science “U. Dini”, University of Florence, Florence, Italy

    Andrea Colesanti

  3. Dept. of Mathematics and Computer Science “U. Dini”, University of Florence, Florence, Italy

    Paolo Gronchi

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Bernig, A., Fu, J.H.G., Solanes, G. (2018). Dual Curvature Measures in Hermitian Integral Geometry. In: Bianchi, G., Colesanti, A., Gronchi, P. (eds) Analytic Aspects of Convexity. Springer INdAM Series, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-71834-7_1

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