Geodesic
A classification of $\operatorname{SL}(n)$ invariant valuations
Monika Ludwig1 ; Matthias Reitzner2
1 Institut für Diskrete Mathematik and Geometrie, TU Wien, Wiedner Hauptstrasse 8-10/104, 1040 Wien, Austria and Department of Mathematics, Polytechnic Institute of New York University, Six Metrotech Center, Brooklyn, New York 11201, United States
2 Fachbereich 6: Mathematik/Informatik, Universität Osnarbück, Albrechtstrasse 28a, 49076 Osnabrück, Germany
Annals of mathematics, Tome 172 (2010) no. 2, pp. 1219-1267.

Voir la notice de l'article provenant de la source Annals of Mathematics website

A classification of upper semicontinuous and $\operatorname{SL}(n)$ invariant valuations on the space of $n$-dimensional convex bodies is established. As a consequence, complete characterizations of centro-affine and $L_p$ affine surface areas are obtained. The proofs make use of a new $\operatorname{SL}(n)$ shaping process for convex bodies.
DOI : 10.4007/annals.2010.172.1219

Monika Ludwig 1 ; Matthias Reitzner 2

1 Institut für Diskrete Mathematik and Geometrie, TU Wien, Wiedner Hauptstrasse 8-10/104, 1040 Wien, Austria and Department of Mathematics, Polytechnic Institute of New York University, Six Metrotech Center, Brooklyn, New York 11201, United States
2 Fachbereich 6: Mathematik/Informatik, Universität Osnarbück, Albrechtstrasse 28a, 49076 Osnabrück, Germany 
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Monika Ludwig; Matthias Reitzner. A classification of $\operatorname{SL}(n)$ invariant valuations. Annals of mathematics, Tome 172 (2010) no. 2, pp. 1219-1267. doi : 10.4007/annals.2010.172.1219. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.1219/

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