## Abstract

Given a positive lower semi-continuous density f on (Formula presented.) the weighted volume (Formula presented.) is defined on the (Formula presented.)-measurable sets in (Formula presented.). The f-weighted perimeter of a set of finite perimeter E in (Formula presented.) is written (Formula presented.). We study minimisers for the weighted isoperimetric problem (Formula presented.)for (Formula presented.). Suppose f takes the form (Formula presented.) where (Formula presented.) is a non-decreasing convex function. Let (Formula presented.) and B a centred ball in (Formula presented.) with (Formula presented.). We show that B is a minimiser for the above variational problem and obtain a uniqueness result.

Original language | English |
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Pages (from-to) | 1-58 |

Number of pages | 58 |

Journal | Ricerche di Matematica |

Early online date | 21 Mar 2018 |

DOIs | |

Publication status | E-pub ahead of print - 21 Mar 2018 |

## Keywords

- Generalised mean curvature
- Isoperimetric problem
- Log-convex density