A general geometric construction for affine surface area

Werner, Elisabeth

Studia Mathematica, Tome 133 (1999), p. 227-238 / Harvested from The Polish Digital Mathematics Library

Résumé

Let K be a convex body in $ℝ^{n}$ and B be the Euclidean unit ball in $ℝ^{n}$ . We show that $l i m_{t \to 0} (| K | - | K_{t} |) / (| B | - | B_{t} |) = a s (K) / a s (B)$ , where as(K) respectively as(B) is the affine surface area of K respectively B and ${K_{t}}_{t \geq 0}$ , ${B_{t}}_{t \geq 0}$ are general families of convex bodies constructed from K,B satisfying certain conditions. As a corollary we get results obtained in [M-W], [Schm], [S-W] and [W].

Publié le : 1999-01-01

Zbl 0927.52008

EUDML-ID : urn:eudml:doc:216596

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     author = {Elisabeth Werner},
     title = {A general geometric construction for affine surface area},
     journal = {Studia Mathematica},
     volume = {133},
     year = {1999},
     pages = {227-238},
     zbl = {0927.52008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv132i3p227bwm}
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Werner, Elisabeth. A general geometric construction for affine surface area. Studia Mathematica, Tome 133 (1999) pp. 227-238. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv132i3p227bwm/

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