Related papers: Local Indicators for Plurisubharmonic Functions

A set of regularly distributed transmission eigenvalues generates a density function. We use such a density function inversely determines the form of the indicator function. Using the entire function theory, we reduce an uniqueness problem…

We prove some results which give sufficient conditions so that pointwise approximation of negative plurisubharmonic functions on complex varieties by continuous plurisubharmonic ones is possible.

Indicator functions mentioned in the title are constructed on an arbitrary nondiscrete locally compact Abelian group of finite dimension. Moreover, they can be obtained by small perturbation from any indicator function fixed beforehand. In…

This paper presents a point-free version of the Lebesgue integral for simple functions on $\sigma$-locales. It describes the integral with respect to a measure defined on the coframe of all $\sigma$-sublocales, moving beyond the constraints…

Let $(X,\omega)$ be a compact K\"ahler manifold. We introduce and study the largest set $DMA(X,\omega)$ of $\omega$-plurisubharmonic (psh) functions on which the complex Monge-Amp\`ere operator is well defined. It is much larger than the…

We solve the Dirichlet problem for the complex Monge-Amp\`ere equation on a strictly pseudoconvex with the right hand side being a positive Borel measure which is dominated by the Monge-Amp\`ere measure of a H\"older continuous…

In this article, we will construct a plurisubharmonic function whose jumping coefficients have a cluster point. We also give a class of plurisubharmonic functions which cannot be equisingular to any plurisubharmonic function with…

We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…

In this article, we study an inverse problem with local data for a linear polyharmonic operator with several lower order tensorial perturbations. We consider our domain to have an inaccessible portion of the boundary where neither the input…

We find an explicit general formula for the iterated local monodromy of singularities of the Hadamard product of functions with integrable singularities. The formula implies the invariance by Hadamard product of the class of functions with…

We present a new approach to the study of multiplier ideals in a local, two-dimensional setting. Our method allows us to deal with ideals, graded systems of ideals and plurisubharmonic functions in a unified way. Among the applications are…

We define the Monge-Amp\`ere operator for continuous J-plurisubharmonic functions on four dimensional almost complex manifolds.

We give a short survey on plurisubharmonic interpolation, with focus on possibility of connecting two given plurisubharmonic functions by plurisubharmonic geodesic.

In this paper, we derive a formula for the pluricomplex Green function of the bidisk with two poles of equal weights. In 2017, Kosi\'nski, Thomas, and Zwonek proved the Lempert function and the pluricomplex Green function are equal on the…

In this paper, we prove a Moser-Trudinger type inequality for pluri-subharmonic functions vanishing on the boundary. Our proof uses a descent gradient flow for the complex Monge-Ampere functional.

We study the minimum sets of plurisubharmonic functions with strictly positive Monge-Amp\`ere densities. We investigate the relationship between their Hausdorff dimension and the regularity of the function. Under suitable assumptions we…

The aim of this paper is to study the Lelong number, the integrability index and the Monge-Amp\`ere mass at the origin of an $S^1$-invariant plurisubharmonic function on a balanced domain in $\mathbb{C}^n$ under the Schwarz symmetrization.…

We show that a positive Borel measure of positive finite total mass, on compact Hermitian manifolds, admits a Holder continuous quasi-plurisubharmonic solution to the Monge-Ampere equation if and only if it is dominated locally by…

This article proves the existence and regularity of weak solutions for a class of mixed local-nonlocal problems with singular nonlinearities. We examine both the purely singular problem and perturbed singular problems. A central…

We prove a comparison principle for the pluripotential complex Monge-Amp\`ere flows for the right-hand side of the form $dt \wedge d\mu$ where $d\mu$ is dominated by a Monge-Amp\`ere measure of a bounded plurisubharmonic function. As a…