### Abstract

Let (X, ω) be a compact Kähler manifold. We introduce and study the largest set DMA(X, ω) of ω-plurisubharmonic (psh) functions on which the complex Monge-Ampère operator is well defined. It is much larger than the corresponding local domain of definition, though still a proper subset of the set PSH(X, ω) of all ω-psh functions. We prove that certain twisted Monge-Ampère operators are well defined for all ω-psh functions. As a consequence, any ω-psh function with slightly attenuated singularities has finite weighted Monge-Ampère energy.

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

Pages (from-to) | 393-418 |

Number of pages | 26 |

Journal | Mathematische Zeitschrift |

Volume | 259 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2008 |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Domains of definition of Monge-Ampère operators on compact Kähler manifolds'. Together they form a unique fingerprint.

## Cite this

Coman, D., Guedj, V., & Zeriahi, A. (2008). Domains of definition of Monge-Ampère operators on compact Kähler manifolds.

*Mathematische Zeitschrift*,*259*(2), 393-418. https://doi.org/10.1007/s00209-007-0233-1