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arXiv · 2610.05937

Local-to-global maximality for plurisubharmonic functions with locally analytic singularities

Thai Duong Do·Pham Hoang Hiep
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Abstract

We prove that a locally maximal plurisubharmonic function on a domain in $\bC^n$, $n\geq2$, is maximal if it has locally analytic singularities with a two-sided locally bounded remainder. McAdam's theorem gives a necessary bound on the analytic spread of the local defining ideals. Comparison on a normalized blow-up then controls the singularities of competing functions. As a consequence, maximality is characterized by the vanishing of the Bedford--Taylor Monge--Ampère measure off the pole set together with the analytic spread bound.

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Thai Duong Do, Pham Hoang Hiep. 2026-10-05. Local-to-global maximality for plurisubharmonic functions with locally analytic singularities. https://arxiv.org/abs/2610.05937

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