The Centro-Affine Hadwiger Theorem

Haberl, Christoph; Parapatits, Lukas

doi:10.1090/S0894-0347-2014-00781-5

The Centro-Affine Hadwiger Theorem
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by Christoph Haberl and Lukas Parapatits

J. Amer. Math. Soc. 27 (2014), 685-705

DOI: https://doi.org/10.1090/S0894-0347-2014-00781-5

Published electronically: January 16, 2014

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Abstract:

All upper semicontinuous and $\mathrm {SL}(n)$ invariant valuations on convex bodies containing the origin in their interiors are completely classified. Each such valuation is shown to be a linear combination of the Euler characteristic, the volume, the volume of the polar body, and the recently discovered Orlicz surface areas.

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