A classification of SL(n) invariant valuations
| Autor(en): | Ludwig, Monika Reitzner, Matthias |
Stichwörter: | AFFINE SURFACE-AREA; BODIES; CONVEX HYPERSURFACES; L-0-MINKOWSKI PROBLEM; L-P; Mathematics; MINKOWSKI-FIREY THEORY; MIXED VOLUMES; MULTIPLICATIVE STRUCTURE; STEPWISE APPROXIMATION; VALUED VALUATIONS | Erscheinungsdatum: | 2010 | Herausgeber: | ANNAL MATHEMATICS | Journal: | ANNALS OF MATHEMATICS | Volumen: | 172 | Ausgabe: | 2 | Startseite: | 1219 | Seitenende: | 1267 | Zusammenfassung: | A classification of upper semicontinuous and 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 SL(n) shaping process for convex bodies. |
ISSN: | 0003486X |
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