The Centro-Affine Hadwiger Theorem

Haberl, Christoph¹ ; Parapatits, Lukas¹

¹ Vienna University of Technology, Institute of Discrete Mathematics and Geometry, Wiedner Hauptstraße 8–10/104, 1040 Wien, Austria

Journal of the American Mathematical Society, Tome 27 (2014) no. 3, pp. 685-705

Résumé

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.

Détail

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

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