Dual area measures and local additive kinematic formulas

  • Andreas BernigEmail author
Original Paper


We prove that higher moment maps on area measures of a euclidean vector space are injective, while the kernel of the centroid map equals the image of the first variation map. Based on this, we introduce the space of smooth dual area measures on a finite-dimensional euclidean vector space and prove that it admits a natural convolution product which encodes the local additive kinematic formulas for groups acting transitively on the unit sphere. As an application of this new integral-geometric structure, we obtain the local additive kinematic formulas in hermitian vector spaces in a very explicit way.


Area measure Valuation Kinematic formula Integral geometry 

Mathematics Subject Classification (2000)

53C65 52A22 



I thank Gil Solanes for many useful comments on a first version of this paper.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Institut für MathematikGoethe-Universität Frankfurt am MainFrankfurtGermany

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