Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 42, No. 1, pp. 263-273 (2001)

On the Busemann Area in Minkowski Spaces

Rolf Schneider

Mathematisches Institut, Albert-Ludwigs-Universität, Eckerstr. 1, 79104 Freiburg i.Br., Germany

Abstract: Among the different notions of area in a Minkowski space, those due to Busemann and to Holmes and Thompson, respectively, have found particular attention. In recent papers it was shown that the Holmes-Thompson area is integral-geometric, in the sense that certain integral-geometric formulas of Crofton-type, well known for the area in Euclidean space, can be carried over to Minkowski spaces and the Holmes-Thompson area. In the present paper, the Busemann area is investigated from this point of view.

Classification (MSC2000): 52A21; 46B20, 52A22, 53C65

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