Width-integrals and affine surface area of convex bodies.

Cheung, Wing-Sum; Zhao, Chang-Jian

Displaying similar documents to “Width-integrals and affine surface area of convex bodies.”

Inequalities for dual affine quermassintegrals.

Yuan, Jun, Leng, Gangsong (2006)

Journal of Inequalities and Applications [electronic only]

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Illumination bodies and affine surface area

Elisabeth Werner (1994)

Studia Mathematica

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We show that the affine surface area as(∂K) of a convex body K in $ℝ^{n}$ can be computed as $a s (\partial K) = l i m_{δ \to 0} d_{n} (v o l_{n} (K^{δ}) - v o l_{n} (K)) / (δ^{2 / (n + 1)})$ where $d_{n}$ is a constant and $K^{δ}$ is the illumination body.

Contributions to Affine Surface Area.

Daniel Hug (1996)

Manuscripta mathematica

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A general geometric construction for affine surface area

Elisabeth Werner (1999)

Studia Mathematica

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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].