The Illumination Body of Almost Polygonal Bodies

Elisabeth Werner

doi:10.1023/A:1004984627126

The Illumination Body of Almost Polygonal Bodies

Elisabeth Werner

Institute for Mathematics and its Applications

Research output: Contribution to journal › Article › peer-review

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Abstract

For a convex body K in R² with illumination body K^δ we consider an expression connected with the affine surface area of K, namely the volume differences vol₂(K^δ) - vol²(K). We investigate what kind of functions can occur as such volume differences and obtain a result similar to the one obtained in the case of floating bodies.

Original language	English (US)
Pages (from-to)	343-354
Number of pages	12
Journal	Geometriae Dedicata
Volume	64
Issue number	3
DOIs	https://doi.org/10.1023/A:1004984627126
State	Published - 1997

Keywords

Affine surface area
Floating body
Illumination body

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10.1023/A:1004984627126

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abstract = "For a convex body K in R2 with illumination body Kδ we consider an expression connected with the affine surface area of K, namely the volume differences vol2(Kδ) - vol2(K). We investigate what kind of functions can occur as such volume differences and obtain a result similar to the one obtained in the case of floating bodies.",

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PY - 1997

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N2 - For a convex body K in R2 with illumination body Kδ we consider an expression connected with the affine surface area of K, namely the volume differences vol2(Kδ) - vol2(K). We investigate what kind of functions can occur as such volume differences and obtain a result similar to the one obtained in the case of floating bodies.

AB - For a convex body K in R2 with illumination body Kδ we consider an expression connected with the affine surface area of K, namely the volume differences vol2(Kδ) - vol2(K). We investigate what kind of functions can occur as such volume differences and obtain a result similar to the one obtained in the case of floating bodies.

KW - Affine surface area

KW - Floating body

KW - Illumination body

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DO - 10.1023/A:1004984627126

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AN - SCOPUS:0043235366

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JO - Geometriae Dedicata

JF - Geometriae Dedicata

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ER -

The Illumination Body of Almost Polygonal Bodies

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Keywords

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