Weighted energy class of $m$-subharmonic functions

H. T. Anh; N. V. Phu; N. Q. Dieu

Weighted energy class of $m$-subharmonic functions

Complex Variables 2024-05-28 v8

Authors: H. T. Anh , N. V. Phu , N. Q. Dieu

Abstract

In this paper, we introduce the class $\mathcal{E}_{m,F}(\Omega)$ and solve complex $m$ -Hessian equations in the class $\mathcal{E}_{m,F}(\Omega)$ . Afterthat, we study subextension in the class $\mathcal{E}_{m,F}(\Omega)$ with the weighted Hessian measure of subextension unchanged. This is an extensive version of the result in [24] in the case when the smaller domain is relatively compact inside the large one.

Keywords

m-subharmonic functions weighted energy class complex m-hessian equations subextension weighted hessian measure

Cite

@article{arxiv.2307.08904,
  title  = {Weighted energy class of $m$-subharmonic functions},
  author = {H. T. Anh and N. V. Phu and N. Q. Dieu},
  journal= {arXiv preprint arXiv:2307.08904},
  year   = {2024}
}

Comments

26 pages(version 8)

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