Convergence in $(\omega,m)$-capacity in the class $\mathcal{E}(X, \omega,m)$ on compact K\"ahler manifolds

Le Mau Hai; Nguyen Van Phu

Convergence in $(\omega,m)$-capacity in the class $\mathcal{E}(X, \omega,m)$ on compact K\"ahler manifolds

Complex Variables 2026-03-30 v1

Authors: Le Mau Hai , Nguyen Van Phu

Abstract

In this paper, we establish the weak*-convergence of a sequence of the complex Hessian measures $H_m(u_j)$ to the complex Hessian measure $H_m(u)$ in the class $\mathcal{E}(X,\omega,m)$ under hypotheses that $u_j$ is convergent to $u$ in $(\omega,m)$ -capacity.

Keywords

Kähler manifolds complex Hessian measures capacity convergence pluripotential theory weak*-convergence Monge-Ampère operator

Cite

@article{arxiv.2603.26392,
  title  = {Convergence in $(\omega,m)$-capacity in the class $\mathcal{E}(X, \omega,m)$ on compact K\"ahler manifolds},
  author = {Le Mau Hai and Nguyen Van Phu},
  journal= {arXiv preprint arXiv:2603.26392},
  year   = {2026}
}

Comments

27 pages, accepted to Mathematical Notes

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