Convergence in $(Ï,m)$-capacity in the class $\mathcal{E}(X, Ï,m)$ on compact KÃ¤hler manifolds

Le Mau Hai; Nguyen Van Phu

paper

Convergence in $(I ¨ , m)$ -capacity in the class $E (X, I ¨ , m)$ on compact KÃ¤hler manifolds

arXiv:2603.26392

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 $E (X, I ¨ , m)$ under hypotheses that $u_{j}$ is convergent to $u$ in $(I ¨ , m)$ -capacity.

27 pages, accepted to Mathematical Notes

Convergence in (I¨,m)-capacity in the class E(X,I¨,m) on compact KÃ¤hler manifolds

Abstract

Convergence in $(I ¨ , m)$ -capacity in the class $E (X, I ¨ , m)$ on compact KÃ¤hler manifolds