A general geometric construction for affine surface area

Elisabeth Werner

doi:10.4064/sm-132-3-227-238

A general geometric construction for affine surface area

Elisabeth Werner

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Abstract

Let K be a convex body in ℝⁿ and B be the Euclidean unit ball in ℝⁿ. We show that lim_t→0 |K| - |K_t|/|B| - |B_t| = as(K)/as(B), where as(K) respectively as(B) is the affine surface area of K respectively B and {K_t}_t≥0, {B_t}_t≥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].

Original language	English (US)
Pages (from-to)	227-238
Number of pages	12
Journal	Studia Mathematica
Volume	132
Issue number	3
DOIs	https://doi.org/10.4064/sm-132-3-227-238
State	Published - 1999
Externally published	Yes

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abstract = "Let K be a convex body in ℝn and B be the Euclidean unit ball in ℝn. We show that limt→0 |K| - |Kt|/|B| - |Bt| = as(K)/as(B), where as(K) respectively as(B) is the affine surface area of K respectively B and \{Kt\}t≥0, \{Bt\}t≥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].",

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T1 - A general geometric construction for affine surface area

AU - Werner, Elisabeth

PY - 1999

Y1 - 1999

N2 - Let K be a convex body in ℝn and B be the Euclidean unit ball in ℝn. We show that limt→0 |K| - |Kt|/|B| - |Bt| = as(K)/as(B), where as(K) respectively as(B) is the affine surface area of K respectively B and {Kt}t≥0, {Bt}t≥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].

AB - Let K be a convex body in ℝn and B be the Euclidean unit ball in ℝn. We show that limt→0 |K| - |Kt|/|B| - |Bt| = as(K)/as(B), where as(K) respectively as(B) is the affine surface area of K respectively B and {Kt}t≥0, {Bt}t≥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].

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JO - Studia Mathematica

JF - Studia Mathematica

IS - 3

ER -

A general geometric construction for affine surface area

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