### Abstract

We prove that the Green equilibrium measure and the Green equilibrium energy of a compact set K relative to the domains D and Ω are the same if and only if D is nearly equal to Ω, for a wide class of compact sets K. Also, we prove that equality of Green equilibrium measures arises if and only if the one domain is related with a level set of the Green equilibrium potential of K relative to the other domain.

Original language | English |
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Pages (from-to) | 593-600 |

Number of pages | 8 |

Journal | Filomat |

Volume | 27 |

Issue number | 4 |

DOIs | |

State | Published - 2013 |

### Keywords

- Equilibrium measure
- Green capacity
- Level sets

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## Cite this

Pouliasis, S. (2013). Invariance of green equilibrium measure on the domain.

*Filomat*,*27*(4), 593-600. https://doi.org/10.2298/FIL1304593P