### Abstract

For a finite metric space V with a metric ρ, let V^{n} be the metric space in which the distance between (a_{1}, . . ., a_{n}) and (b_{1}, . . ., b_{n}) is the sum ∑^{n}_{i=1} ρ(a_{i}, b_{i}). We obtain an asymptotic formula for the logarithm of the maximum possible number of points in V^{n} of distance at least d from a set of half the points of V^{n}, when n tends to infinity and d satisfies d ≫ √n.

Original language | English (US) |
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Pages (from-to) | 411-436 |

Number of pages | 26 |

Journal | Geometric and Functional Analysis |

Volume | 8 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1998 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Analysis
- Geometry and Topology

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## Cite this

Alon, N., Boppana, R., & Spencer, J. (1998). An asymptotic isoperimetric inequality.

*Geometric and Functional Analysis*,*8*(3), 411-436. https://doi.org/10.1007/s000390050062