### Abstract

The following containment theorem is presented: If K and L are convex bodies such that every simplex that contains L also contains some translate of K, then in fact the body L must contain a translate of the body K. One immediate consequence of this theorem is a strengthened version of Weil's mixed-volume characterization of containment.

Original language | English (US) |
---|---|

Pages (from-to) | 229-235 |

Number of pages | 7 |

Journal | Discrete and Computational Geometry |

Volume | 19 |

Issue number | 2 |

State | Published - 1998 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology

### Cite this

*Discrete and Computational Geometry*,

*19*(2), 229-235.

**Containment and circumscribing simplices.** / Lutwak, E.

Research output: Contribution to journal › Article

*Discrete and Computational Geometry*, vol. 19, no. 2, pp. 229-235.

}

TY - JOUR

T1 - Containment and circumscribing simplices

AU - Lutwak, E.

PY - 1998

Y1 - 1998

N2 - The following containment theorem is presented: If K and L are convex bodies such that every simplex that contains L also contains some translate of K, then in fact the body L must contain a translate of the body K. One immediate consequence of this theorem is a strengthened version of Weil's mixed-volume characterization of containment.

AB - The following containment theorem is presented: If K and L are convex bodies such that every simplex that contains L also contains some translate of K, then in fact the body L must contain a translate of the body K. One immediate consequence of this theorem is a strengthened version of Weil's mixed-volume characterization of containment.

UR - http://www.scopus.com/inward/record.url?scp=0032392884&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032392884&partnerID=8YFLogxK

M3 - Article

VL - 19

SP - 229

EP - 235

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 2

ER -