Extensions of translation invariant valuations on polytopes

We study translation invariant, real-valued valuations on the class of convex polytopes in Euclidean space and discuss which continuity properties are sufficient for an extension of such valuations to all convex bodies. For this purpose, we introduce flag support measures of convex bodies via a loca...

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Veröffentlicht in:	arXiv.org 2014-04
Hauptverfasser:	Hinderer, Wolfram, Hug, Daniel, Weil, Wolfgang
Format:	Artikel
Sprache:	eng
Schlagworte:	Euclidean geometry Euclidean space Invariants Mathematics - Metric Geometry Polytopes
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Zusammenfassung:	We study translation invariant, real-valued valuations on the class of convex polytopes in Euclidean space and discuss which continuity properties are sufficient for an extension of such valuations to all convex bodies. For this purpose, we introduce flag support measures of convex bodies via a local Steiner formula and derive some of the properties of these measures.
ISSN:	2331-8422
DOI:	10.48550/arxiv.1303.4406