Polar sets for $m$-subharmonic functions on compact Hermitian manifolds

Fuente: arXiv
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Main Authors: Kolodziej, Slawomir, Nguyen, Ngoc Cuong
Format: Preprint
Published: 2025
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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
id 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