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A Characterization of Affine Surface Area  (Make Corrections)  (2 citations)
Monika Ludwig, Matthias Reitzner



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Abstract: We show that every upper semicontinuous and equi-ane invariant valuation on the space of d-dimensional convex bodies is a linear combination of ane surface area, volume and the Euler characteristic. (Update)

Cited by:   More
Ellipsoids and Matrix Valued Valuations - Ludwig (2003)   (Correct)
Upper Semicontinuous Valuations on the Space of Convex Discs - Ludwig   (Correct)

Active bibliography (related documents):   More   All
2.7:   A Characterization of Affine Length and Asymptotic Approximation.. - Ludwig   (Correct)
1.0:   A Helmholtz-Lie Type Characterization of Ellipsoids II - Gruber, Ludwig   (Correct)
0.7:   Asymptotic Approximation by Quadratic Spline Curves - Ludwig   (Correct)

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BibTeX entry:   (Update)

M. Ludwig and M. Reitzner, A characterization of ane surface area, Adv. Math., to appear. http://citeseer.ist.psu.edu/747203.html   More

@misc{ ludwig-characterization,
  author = "M. Ludwig and M. Reitzner",
  title = "A characterization of ane surface area",
  text = "M. Ludwig and M. Reitzner, A characterization of ane surface area, Adv.
    Math., to appear.",
  url = "citeseer.ist.psu.edu/747203.html" }
Citations (may not include all citations):
144   Convex bodies: the Brunn{Minkowski theory (context) - Schneider - 1993
94   The geometry of fractal sets (context) - Falconer - 1985
59   Lectures on functional equations and their applications (context) - Aczel - 1966
25   Introduction to geometric probability (context) - Klain, Rota - 1997
17   Aspects of approximation of convex bodies (context) - Gruber - 1993
11   ache und Isoperimetrie (context) - Hadwiger, uber et al. - 1957
8   Theory of the integral (context) - Saks - 1964
8   Valuations on convex bodies (context) - McMullen, Schneider - 1983
6   Valuations and dissections (context) - McMullen - 1993
6   Ane geometry of convex bodies (context) - Leichtwei - 1998
5   Comparisons of best and random approximation of convex bodie.. (context) - Gruber - 1997
5   New results in the theory of packing and covering (context) - Fejes, oth - 1983
4   A short proof of Hadwiger's characterization theorem (context) - Klain - 1995
3   A characterization of ane length and asymptotic approximatio.. (context) - Ludwig
3   Analytische Eigenschaften konvexer Funktionen auf Riemannsch.. (context) - Bangert - 1979
3   Extended ane surface area (context) - Lutwak - 1991
2   Equality of two representations of extended ane surface area (context) - Dolzmann, Hug - 1995
2   Contributions to ane surface area (context) - Hug - 1996
2   Selected ane isoperimetric inequalities (context) - Lutwak - 1993
2   The Santalo-regions of a convex body (context) - Meyer, Werner - 1998
2   Zur Anober ache konvexer Korper (context) - Leichtwei - 1986
2   Geominimal surface area (context) - Petty - 1974
2   Bemerkungen zur De nition einer erweiterten Anober ache von.. (context) - Leichtwei - 1989
2   Almost everywhere existence of the second di erential of a c.. (context) - Aleksandrov - 1939
2   the ane surface area (context) - Sch, On - 1993
1   uber Integralgeometrie (context) - Blaschke - 1937
1   Curvature measures of convex bodies (context) - Schneider - 1978
1   erentialgeometrie II: Ane Di erentialgeometrie (context) - Blaschke - 1923
1   The convex oating body (context) - Sch, Werner - 1990
1   Uber eine Formel Blaschkes zur Anober ache (context) - Leichtwei - 1986
1   A general geometric construction for ane surface area (context) - Werner - 1998

Documents on the same site (http://www.dmg.tuwien.ac.at/ludwig/ludwig_pub.html):   More
Upper Semicontinuous Valuations on the Space of Convex Discs - Ludwig   (Correct)
Asymptotic Approximation of Convex Curves; the Hausdorff Metric.. - Ludwig   (Correct)
Moment Vectors of Polytopes - Ludwig   (Correct)

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