6 papers
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…
On Lelong numbers of plurisubharmonic functions on complex spaces
Le Mau Hai, Pham Hoang Hiep, Trinh Tung
In this paper, we introduce the notion of strong locally irreducible complex spaces . Based on this notion we prove the equality mult$(\widetilde{X},x)…
Singularity invariants of plurisubharmonic functions and complex spaces
Pham Hoang Hiep
In this paper, we combine tools from pluripotential theory and commutative algebra to study singularity invariants of plurisubharmonic functions. We establish several relationships…
Monge-Ampere measures on subvarieties
Per Ahag, Urban Cegrell, Pham Hoang Hiep
In this article we address the question whether the complex Monge-Ampère equation is solvable for measures with large singular part. We prove that under some conditions there are n…
The weighted log canonical threshold
Pham Hoang Hiep
In this note, we show how to apply the original -extension theorem of Ohsawa and Takegoshi to the standard basis of a multiplier ideal sheaf associated with a plurisubharmonic…