A general geometric construction for affine surface area

Elisabeth Werner

Displaying similar documents to “A general geometric construction for affine surface area”

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.

Support functions of central convex bodies

Lindquist, Norman F. (1975)

Portugaliae mathematica

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Approximation of convex bodies by sums of line segments

Lindquist, Norman F. (1975)

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Spherical and ellipsoidality theorems for convex bodies

Dorn, C. (1978)

Portugaliae mathematica

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The mean surface area of the boxes circumscribed about a convex body

Rolf Schneider (1972)

Annales Polonici Mathematici

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Parallelepipeds circumscribed about a convex body in 3-space.

Makeev, V.V. (2005)

Journal of Mathematical Sciences (New York)

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Some geometric inequalities for the Holmes-Thompson definitions of volume and surface area in Minkowski spaces.

Mustafaev, Zokhrab (2004)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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The skeleta of convex bodies

David G. Larman (2009)

Banach Center Publications

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The connectivity and measure theoretic properties of the skeleta of convex bodies in Euclidean space are discussed, together with some long standing problems and recent results.