Polar sets for $m$-subharmonic functions on compact Hermitian manifolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912683510464512 |
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| author | Kolodziej, Slawomir Nguyen, Ngoc Cuong |
| author_facet | Kolodziej, Slawomir Nguyen, Ngoc Cuong |
| contents | We prove a sharp decay of capacity of sublevel sets of a $(ω,m)$-subharmonic functions on a $n$-dimensional compact Hermitian manifold $(X,ω)$ which generalizes the case $m=n$ as well as the case $1\leq m\leq n$ on a compact Kähler manifold. We also obtain the full characterizations of polar sets of such functions in terms of the corresponding local and global capacities, and of the extremal functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_01159 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polar sets for $m$-subharmonic functions on compact Hermitian manifolds Kolodziej, Slawomir Nguyen, Ngoc Cuong Complex Variables Analysis of PDEs Differential Geometry We prove a sharp decay of capacity of sublevel sets of a $(ω,m)$-subharmonic functions on a $n$-dimensional compact Hermitian manifold $(X,ω)$ which generalizes the case $m=n$ as well as the case $1\leq m\leq n$ on a compact Kähler manifold. We also obtain the full characterizations of polar sets of such functions in terms of the corresponding local and global capacities, and of the extremal functions. |
| title | Polar sets for $m$-subharmonic functions on compact Hermitian manifolds |
| topic | Complex Variables Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2511.01159 |