## Abstract

Let K be a convex body in ℝ^{n}with centroid at 0 and B be the Euclidean unit ball in ℝ^{n}centered at 0. We show that lim_{t→0}|K|-|K_{t}|/|B| _|B_{t}| =O_{p}(K)/O_{p}(B) where |K| respectively |B| denotes the volume of K respectively B, O_{p}(K) respectively O_{p}(B) is the p-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 [23,25,26,31]. Indiana University Mathematics Journal

Original language | English (US) |
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Pages (from-to) | 2305-2323 |

Number of pages | 19 |

Journal | Indiana University Mathematics Journal |

Volume | 56 |

Issue number | 5 |

DOIs | |

State | Published - 2007 |

Externally published | Yes |

## Keywords

- Affine surface area

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