Pluripotential theory

In this article "Convergence in capacity and applications", the authors prove that if uj , vj , w ∈ E () such that uj , vj ≥ w, ∀ j ≥ 1, and |uj − vj | → 0 in Cn-capacity, then limj→∞ h(ϕ1,...,ϕm)[(ddcuj )n − (ddcvj )n] = 0 in the weak-topology of measures for all ϕ1,...,ϕm ∈ PSH ∩L∞ loc(), h ∈ C(Rm). We shall then use this result to give some applications.

13p runordie5 04-07-2022 8 2   Download

The aim of the paper "Uniqueness properties of m-subharmonic functions in Cegrell classes" is to provide sufficient conditions for unicity of m-subharmonic functions. Since two plurisubharmonic functions may equal on an open subset of a domain without being identical (e.g. u ≡ 0 and v(z) = max(log |z|, 0)), it seems natural to put additional assumptions on Hessian measures of u and v to guarantee that u ≡ v on the whole domain Ω.

15p runordie3 27-06-2022 23 2   Download

The dissertation is written on the basis of the paper published in Annales Polonici Mathematici, the paper published in Acta Mathematica Vietnamica and the paper published in Results in Mathematics.

65p caphesuadathemtieu 02-03-2022 18 4   Download

Research Article An Inequality for the Beta Function with Application to Pluripotential Theory

8p dauphong17 22-02-2012 40 3   Download