Illumination bodies and affine surface area

Elisabeth Werner

Studia Mathematica (1994)

  • Volume: 110, Issue: 3, page 257-269
  • ISSN: 0039-3223

Abstract

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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 ( ∂ K ) = l i m δ → 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.

How to cite

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Werner, Elisabeth. "Illumination bodies and affine surface area." Studia Mathematica 110.3 (1994): 257-269. <http://eudml.org/doc/216113>.

@article{Werner1994,
abstract = {We show that the affine surface area as(∂K) of a convex body K in $ℝ^\{n\}$ can be computed as $as(∂K) = lim_\{δ→0\} d_\{n\} (vol_\{n\}(K^\{δ\}) - vol_\{n\}(K))/(δ^\{2/(n+1)\})$ where $d_\{n\}$ is a constant and $K^\{δ\}$ is the illumination body.},
author = {Werner, Elisabeth},
journal = {Studia Mathematica},
keywords = {illumination body; affine surface area; convex floating body},
language = {eng},
number = {3},
pages = {257-269},
title = {Illumination bodies and affine surface area},
url = {http://eudml.org/doc/216113},
volume = {110},
year = {1994},
}

TY - JOUR
AU - Werner, Elisabeth
TI - Illumination bodies and affine surface area
JO - Studia Mathematica
PY - 1994
VL - 110
IS - 3
SP - 257
EP - 269
AB - We show that the affine surface area as(∂K) of a convex body K in $ℝ^{n}$ can be computed as $as(∂K) = lim_{δ→0} d_{n} (vol_{n}(K^{δ}) - vol_{n}(K))/(δ^{2/(n+1)})$ where $d_{n}$ is a constant and $K^{δ}$ is the illumination body.
LA - eng
KW - illumination body; affine surface area; convex floating body
UR - http://eudml.org/doc/216113
ER -

References

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  1. [B] W. Blaschke, Vorlesungen über Differentialgeometrie II, Springer, 1923. Zbl49.0499.01
  2. [H] R. Howard, personal communication. 
  3. [L1] K. Leichtweiss, Über ein Formel Blaschkes zur Affinoberfläche, Studia Sci. Math. Hungar. 21 (1986), 453-474. Zbl0561.53012
  4. [L2] K. Leichtweiss, Zur Affinoberfläche konvexer Körper, Manuscripta Math. 56 (1986), 429-464. 
  5. [Lu] E. Lutwak, Extended affine surface area, Adv. in Math. 85 (1991), 39-68. Zbl0727.53016
  6. [SW] C. Schütt and E. Werner, The convex floating body, Math. Scand. 66 (1990), 275-290. Zbl0739.52008

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