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Integral Geometry in Minkowski Spaces

✍ Scribed by Rolf Schneider; John André Wieacker

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
481 KB
Volume
129
Category
Article
ISSN
0001-8708

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✦ Synopsis

We investigate the possibility of extending classical integral geometric results, involving lower-dimensional areas, from Euclidean space to Minkowski spaces (finite-dimensional Banach spaces). Of the two natural notions of area in a Minkowski space, due respectively to Busemann and to Holmes and Thompson, the latter turns out to be the more tractable one. For the Holmes Thompson area, we derive a translative intersection formula and, in the class of hypermetric Minkowski spaces, full analogues of the Crofton formulae for rectifiable sets and for convex bodies. For the Busemann k-area, we give a short proof of the fact that it coincides, for k-rectifiable sets, with the k-dimensional Hausdorff measure induced by the Minkowski metric.

1997 Academic Press | E j n * k+ j&n (A & E) d+ j (E)=a nkj * k (A)

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