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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…
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…
Sets of cardinality seven are not sum-dominant
Thai Duong Do, Van Thien Nguyen
We give a self-contained elementary proof of the known result that every set of cardinality seven satisfies . The argument adapts Hegarty's method, usi…
Minimal m-subharmonic functions with nonmaximal Hessian measures
Thai Duong Do, Van Thien Nguyen
For every , we construct Hölder continuous functions on the closed unit ball that are minimal in the Cegrell class $\F_m$, although their Hessian measures are not maxi…
Comparison principles for Monge-Ampère measures on pluripolar sets
Thai Duong Do, Hoang Hiep Pham
In this paper, we introduce a notion of singularity comparison for plurisubharmonic functions based on the Bedford--Taylor capacity. We establish comparison principles for the comp…