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On surface area measures of convex bodies

On surface area measures of convex bodies The set L j of jth-order surface area measures of convex bodies in d-space is well known for j=d−1. A characterization of L j was obtained by Firey and Berg. The determination of L j, for j∈{2, ..., d−2}, is an open problem. Here we show some properties of L j concerning convexity, closeness, and size. Especially we prove that the difference set L j−L j is dense (in the weak topology) in the set of signed Borel measures on the unit sphere which have barycentre 0. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geometriae Dedicata Springer Journals

On surface area measures of convex bodies

Weil, Wolfgang
Geometriae Dedicata , Volume 9 (3) – Jul 7, 2004
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References (14)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Convex and Discrete Geometry; Differential Geometry; Algebraic Geometry; Hyperbolic Geometry; Projective Geometry; Topology
ISSN
0046-5755
eISSN
1572-9168
DOI
10.1007/BF00181175
Publisher site
See Article on Publisher Site

Abstract

The set L j of jth-order surface area measures of convex bodies in d-space is well known for j=d−1. A characterization of L j was obtained by Firey and Berg. The determination of L j, for j∈{2, ..., d−2}, is an open problem. Here we show some properties of L j concerning convexity, closeness, and size. Especially we prove that the difference set L j−L j is dense (in the weak topology) in the set of signed Borel measures on the unit sphere which have barycentre 0.

Journal

Geometriae Dedicata – Springer Journals

Published: Jul 7, 2004

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