Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Kolodziej, Slawomir, Nguyen, Ngoc Cuong
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416435103
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