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math.CV2026
Comparison principles for local plurisubharmonic potentials on complex manifolds and applications
Thai Duong Do, Pham Hoang Hiep
We prove a weighted comparison principle for local plurisubharmonic potentials in Cegrell's class on an arbitrary complex manifold under suitable boundary and gluing conditions. We…
math.CV2026
Local-to-global maximality for plurisubharmonic functions with locally analytic singularities
Thai Duong Do, Pham Hoang Hiep
We prove that a locally maximal plurisubharmonic function on a domain in $\bC^n$, , is maximal if it has locally analytic singularities with a two-sided locally bounded rem…