Weak convergence of complex Monge-Ampère operators on compact Hermitian manifolds
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| Format: | Preprint |
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2024
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| _version_ | 1866916525545357312 |
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| author | Pang, Kai Sun, Haoyuan Wang, Zhiwei |
| author_facet | Pang, Kai Sun, Haoyuan Wang, Zhiwei |
| contents | Let $(X,ω)$ be a compact Hermitian manifold and let $\{β\}\in H^{1,1}(X,\mathbb R)$ be a real $(1,1)$-class with a smooth representative $β$, such that $\int_Xβ^n>0$. Assume that there is a bounded $β$-plurisubharmonic function $ρ$ on $X$. First, we provide a criterion for the weak convergence of non-pluripolar complex Monge-Ampère measures associated to a sequence of $β$-plurisubharmonic functions. Second, this criterion is utilized to solve a degenerate complex Monge-Ampère equation with an $L^1$-density. Finally, an $L^\infty$-estimate of the solution to the complex Monge-Ampère equation for a finite positive Radon measure is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11547 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak convergence of complex Monge-Ampère operators on compact Hermitian manifolds Pang, Kai Sun, Haoyuan Wang, Zhiwei Complex Variables Let $(X,ω)$ be a compact Hermitian manifold and let $\{β\}\in H^{1,1}(X,\mathbb R)$ be a real $(1,1)$-class with a smooth representative $β$, such that $\int_Xβ^n>0$. Assume that there is a bounded $β$-plurisubharmonic function $ρ$ on $X$. First, we provide a criterion for the weak convergence of non-pluripolar complex Monge-Ampère measures associated to a sequence of $β$-plurisubharmonic functions. Second, this criterion is utilized to solve a degenerate complex Monge-Ampère equation with an $L^1$-density. Finally, an $L^\infty$-estimate of the solution to the complex Monge-Ampère equation for a finite positive Radon measure is given. |
| title | Weak convergence of complex Monge-Ampère operators on compact Hermitian manifolds |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2412.11547 |