Related papers: Value distribution and potential theory

This is the first part of a series of three papers. In this paper, we establish a Big Picard type theorem for holomorphic maps $f:Y \to X$, where $Y$ is a ramified covering of the punctured disc $\mathbb{D}^*$ with small ramification and…

In this thesis, we study value distribution theoretical properties of the Gauss map of pseudo-algebraic minimal surfaces in n-dimensional Euclidean space. After reviewing basic facts, we give estimates for the number of exceptional values…

In this paper, we prove a lemma on logarithmic derivative for holomorphic curves from annuli into K\"{a}hler compact manifold and. As its application, a second main theorem for holomophic curves from annuli into semi abelian varieties…

This survey will appear in Vol. VII of the Hendbook of Teichm{\"u}ller theory (European Mathematical Society Publishing House, 2020). It is a commentary on Teichm{\"u}ller's paper "Einfache Beispiele zur Wertverteilungslehre", published in…

The tropical Nevanlinna theory is Nevanlinna theory for tropical functions or maps over the max-plux semiring by using the approach of complex analysis. The main purpose of this paper is to study the second main theorem with tropical…

We give a short survey on generalizations of Nevanlinna's theorems on zero distribution of bounded holomorphic functions and representation of meromorphic functions in multiply connected domains. It is a part of our report in the conference…

We propose a Wigner quasiprobability distribution function for Hamiltonian systems in spaces of constant curvature --in this paper on hyperboloids--, which returns the correct marginals and has the covariance of the Shapiro functions under…

Quasiprobability representations are well-established tools in quantum information science, with applications ranging from the classical simulability of quantum computation to quantum process tomography, quantum error correction, and…

In this paper we present a surprisingly general extension of the main result of a paper that appeared in this journal: I. Montes et al., Sklar's theorem in an imprecise setting, Fuzzy Sets and Systems, 278 (2015), 48--66. The main tools we…

We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…

This paper re-develops the Nevanlinna theory for meromorphic functions on $\mathbb C$ in the viewpoint of holomorphic forms. According to our observation, Nevanlinna's functions can be formulated by a holomorphic form. Applying this thought…

These notes provide an exposition on obtaining the well-known standard results of quasiregular maps on Riemannian manifolds, given the corresponding theory in the Euclidean setting. We recall several different approaches to first-order…

By using techniques of holomorphic jets and Jacobian fields, we devise a non-equidistribution theory of holomorphic curves into complex projective varieties intersecting normal crossing divisors. Based on this theory established, we prove…

In this paper, we want to give an exposition of our recent work on linear and nonlinear potential theory and their applications in conformal geometry. We use potential theory to study linear and quasilinear equations arising from conformal…

In this paper, we generalize the classical Nevanlinna theory of algebroid functions from $\mathbb C$ to a complete K\"ahler manifold with either non-negative Ricci curvature or non-positive sectional curvature. As its applications, we…

In this paper, we introduce the notions of a vector-valued almost automorphic distribution and a vector-valued almost automorphic ultradistribution, working in the framework of complex Banach spaces. We prove several structural…

We develop complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds. This, in particular, includes the results on holomorphic extension from complex submanifolds, corona type theorems,…

This paper use Nevanlinna's Second Main Theorem of the value distribution theory, we got an important conclusion by Riemann hypothesis. this conclusion contradicts the Theorem 8.12 in Titchmarsh's book "Theory of the Riemann…

Consider the empirical spectral distribution of complex random $n\times n$ matrix whose entries are independent and identically distributed random variables with mean zero and variance $1/n$. In this paper, via applying potential theory in…

Many results of the Fatou-Julia iteration theory of rational functions extend to uniformly quasiregular maps in higher dimensions. We obtain results of this type for certain classes of quasiregular maps which are not uniformly quasiregular.