#### Document Type

Article

#### Date

5-31-2007

#### Embargo Period

11-10-2011

#### Disciplines

Mathematics

#### Description/Abstract

Let (X, w) be a compact Kahler manifold. We introduce and study the largest set DMA(X, w) of w-plurisubharmonic (psh) functions on which the complex Monge-Ampere 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, w) of all w-psh functions. We prove that certain twisted Monge-Ampere operators are well defined for all w-psh functions. As a consequence, any w-psh function with slightly attenuated singularities has finite weighted Monge-Ampere energy.

#### Recommended Citation

Coman, Dan; Guedj, Vincent; and Zeriahi, Ahmed, "Domains of Definition of Monge-Ampère Operators on Compact Kähler Manifolds" (2007). *Mathematics Faculty Scholarship.* Paper 20.

http://surface.syr.edu/mat/20

#### Source

Harvested from arXiv.org

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.

## Additional Information

This manuscript is from arXiv.org, for more information look at http://arxiv.org/abs/0705.4529