Abstract
In 1986 the author introduced a notion of equiaffinely invariant surface area Oaff(∂K) for the boundary of an arbitrary compact convex body K in the n-dimensional euclidean space Rn. Independently E.LUTWAK defined such an affine surface area Ω(∂K) for δK in 1988 in a quite different manner.These two definitions are compared with each other in the following article. It turns out that Oaff(∂K) coincides with a modified expression\(\widetilde\Omega (\partial K)\) where\(\widetilde\Omega (\partial K) \leqslant \Omega (\partial K)\), but with equality in the classical case.\(\widetilde\Omega (\partial K)\) has properties as good as Ω(∂K).
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Herrn Bodo Volkmann zum 60. Geburtstag gewidmet
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Leichtweiß, K. Bemerkungen zur Definition einer erweiterten Affinoberfläche von E. Lutwak. Manuscripta Math 65, 181–197 (1989). https://doi.org/10.1007/BF01168298
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DOI: https://doi.org/10.1007/BF01168298