Hessian measures on m-polar sets and applications to the complex Hessian equations

Abstract

In this paper, we first study the convergence in m-capacity. These results are used to obtain an extension of a Kolodziej’s result and Ahag et al.’s result to the class .

Keywords:

• Convergence in capacity
• plurisubharmonic functions
• m-subharmonic functions
• complexm-Hessian operator
• complex Monge–Ampère operator
• m-Hessian equations
• m-polar sets
• m-hyperconvex domain
• Radon measure
• positive measures

AMS Subject Classifications:

• 32U05
• 32U15
• 32U40
• 32W20

Acknowledgements

The authors would like to thank Professor Pham Hoang Hiep for valuable comments during the preparation of this work. The paper was done while the authors were visiting Vietnam Institute for Advanced Study in Mathematics (VIASM). The author would like to thank the VIASM for hospitality and support.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Vietnam Institute for Advanced Study in Mathematics (VIASM) [grant number ViAsM15.81].