Subextension of plurisubharmonic functions with weak singularities

By U. Cegrell, S. Kołodziej, Ahmed Zeriahi. 2004

60 citations recorded by the source corpus.

We prove several results showing that plurisubharmonic functions with various bounds on their Monge-Ampere masses on a bounded hyperconvex domain always admit global plurisubharmonic subextension with logarithmic growth at infinity.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8710520f18c1dac901e8d23d5b362e26763531d5

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Monge–Ampère measures on pluripolar sets (2007, background): “In [2], B locki proved that E = {ϕ ∈ PSH() ∩ W 1,2 loc () : ϕ ≤ 0} when n = 2, and showed that this equality is not valid for n ≥ 3. Later, in [3], he obtained a complete characterization of E for n ≥ 1. Another characterization of E was proved in [ 9 ] in terms of the so-called ϕ-capacity.”
Hessian measures on m-polar sets and applications to the complex Hessian equations (2017, unknown): “3 in [20], we have um,α ∈ Em( ), ∀0 < α < 1 m .”
Partial pluricomplex energy and integrability exponents of plurisubharmonic functions (2008, background): “We will also need the following estimates on the capacity of the sub-level sets of functions in E1(Ω) (see [9]).”
Plurisubharmonic functions with weak singularities (2008, background): “The inequalities (2.1) was proved for psh test functions in [K3] (see also [ CKZ ] and [EGZ]).”