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, Volume 65, Issue 2, pp 181–197 | Cite as

Bemerkungen zur Definition einer erweiterten Affinoberfläche von E. Lutwak

  • Kurt Leichtweiß


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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  1. [1]
    Bauer,H., Wahrscheinlichkeitstheorie und Grundzüge der Maßtheorie, de Gruyter Berlin 1974Google Scholar
  2. [2]
    Blaschke,W.,Vorlesungen über Differentialgeometrie II,Springer Berlin 1923Google Scholar
  3. [3]
    Hardy,Littlewood,Polya,Inequalities,Cambridge Univ.Press 1934Google Scholar
  4. [4]
    Leichtweiß,K.,Zur Affinoberfläche konvexer Körper,Manuscr.Math.56 (1986), 429–464Google Scholar
  5. [5]
    Leichtweiß,K.,Über einige Eigenschaften der Affinoberfläche beliebiger konvexer Körper,Result.Math.13 (1988),255–282Google Scholar
  6. [6]
    Lutwak,E., Extended affine surface area,Preprint 1988Google Scholar
  7. [7]
    Santalo,L.,Un invariante afin para los cuerpos convexos del espacio de n dimensiones,Portug.Math.8 (1949),155–161Google Scholar
  8. [8]
    Schneider,R.,Boundary structure and curvature of convex bodies,Proc.Geom.Symp.Siegen 1978 ed. by J.Tölke and J.Wills, 13–59Google Scholar
  9. [9]
    Simon,L.,Lectures on geometric measure theory, Proc.Centre Math.Anal.Austral.Nat.Univ.3 (1983),1–272Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Kurt Leichtweiß
    • 1
  1. 1.Mathematisches Institut BUniversität StuttgartStuttgart

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