相关论文: Some applications of Projective Logarithmic Potent…
We generalize several known stability estimates for complex Monge-Amp\`ere equations to the setting of low (or high) energy potentials. We apply our estimates to obtain, among other things, a quantitative domination principle, and metric…
In this paper, we prove a $\partial\bar{\partial}$-type lemma on compact K\"ahler manifolds for logarithmic differential forms valued in the dual of a certain pseudo-effective line bundle, thereby confirming a conjecture proposed by X. Wan.…
We give a survey of computation of the conformal capacity of planar condensers, generalized capacity, and logarithmic capacity with emphasis on our recent work 2020-2025. We also discuss some applications of our method based on the boundary…
Finite energy pluripotential theory accommodates the variational theory of equations of complex Monge-Amp\`ere type arising in K\"ahler geometry. Recently it has been discovered that many of the potential spaces involved have a rich metric…
In the context of Dirichlet type spaces on the unit ball of $\mathbb{C}^d$, also known as Hardy-Sobolev or Besov-Sobolev spaces, we compare two notions of smallness for compact subsets of the unit sphere. We show that the functional…
The real and imaginari parts of the Cauchy kernel in the plane are scalar Riesz kernels of homogeneity -1. One can associate with each of them a natural notion of capacity related to bounded potentials. The main result of the paper asserts…
We establish a general variational formula for the logarithmic potential of the free additive convolution of two compactly supported probability measure on $\R$. The formula is given in terms of the $R$-transform of the first measure, and…
We develop a theory of motives with compact support for logarithmic schemes over a field. Starting from the notion of finite logarithmic correspondences with compact support, we define the logarithmic motive with compact support analogous…
The notion of potential output purity of a completely positive map is introduced as a generalization of the regularized output purity. An upper bound is derived for this quantity, and for several classes of maps (including CQ, QC and…
We consider logarithmic averages, over friable integers, of non-negative multiplicative functions. Under logarithmic, one-sided or two-sided hypotheses, we obtain sharp estimates that improve upon known results in the literature regarding…
Riesz Theorem establishes a correspondence between the set of $\sigma$-additive regular Borel measures and the set of linear positively defined functionals. We consider an idempotent analogue of this correspondence between possibility…
The aim of this note is to study the convergence in capacity for functions in the class $\mathcal E(X,\omega)$. We obtain several stability theorems. Some of these are (optimal) generalizations of results of Xing, while others are new.
The concept of a primitive potential for the Schroedinger operator on the line was introduced in [2,3,4]. Such a potential is determined by a pair of positive functions on a finite interval, called the dressing functions, which are not…
Given a model of the theory of the real field with restricted analytic functions such that its value group has finite archimedean rank we show how one can extend the restricted logarithm to a global logarithm with values in the polynomial…
The zero range potential is constructed for a system of two particles interacting via the Coulomb potential. The singular part of the asymptote of the wave function at the origin which is caused by the common effect of the zero range…
We present a numerical method for computing the logarithmic capacity of compact subsets of $\mathbb{C}$, which are bounded by Jordan curves and have finitely connected complement. The subsets may have several components and need not have…
We generalize some aspects of the theory of compact projections relative to a C*-algebra, to the setting of more general algebras. Our main result is that compact projections are the decreasing limits of `peak projections', and in the…
We study the hole probabilities of the infinite Ginibre ensemble ${\mathcal X}_{\infty}$, a determinantal point process on the complex plane with the kernel $\mathbb K(z,w)= \frac{1}{\pi}e^{z\bar w-\frac{1}{2}|z|^2-\frac{1}{2}|w|^2}$ with…
We verify an old conjecture of G. Polya and G. Szego saying that the regular n-gon minimizes the logarithmic capacity among all n-gons with a fixed area.
We prove the finiteness of relative log pluricanonical representations in the complex analytic setting. As an application, we discuss the abundance conjecture for semi-log canonical pairs within this framework. Furthermore, we establish the…