A Uniqueness Theorem of Meromorphic Maps and a Generalization of the Borel’s Lemma

2019 ◽  
Vol 35 (9) ◽  
pp. 1464-1480
Author(s):  
Kai Zhou ◽  
Lu Jin
Keyword(s):  
Uniqueness Theorem ◽  
Meromorphic Maps

scholarly journals A uniqueness theorem of algebraically non-degenerate meromorphic maps into PN(C)

1976 ◽  
Vol 64 ◽  
pp. 117-147 ◽  
Author(s):  
Hirotaka Fujimoto
Keyword(s):  
Projective Space ◽  
Uniqueness Theorem ◽  
Complex Projective Space ◽  
Meromorphic Functions ◽  
Uniqueness Theorems ◽  
Meromorphic Maps ◽  
Complex Projective

In the previous paper [3], the author generalized the uniqueness theorems of meromorphic functions given by G. Pólya in [5] and R. Nevanlinna in [4] to the case of meromorphic maps of Cn into the N- dimensional complex projective space PN(C).

scholarly journals Remarks to the uniqueness problem of meromorphic maps into PN(C), II

1978 ◽  
Vol 71 ◽  
pp. 25-41 ◽  
Author(s):  
Hirotaka Fujimoto
Keyword(s):  
Uniqueness Theorem ◽  
Meromorphic Functions ◽  
Uniqueness Problem ◽  
Meromorphic Maps

In [7], R. Nevanlinna gave the following uniqueness theorem of meromorphic functions as an improvement of a result of G. Pólya ([8]).Theorem A. Let f, g be non-constant meromorphic functions on C. If there are five mutually distinct values a1, …, a5 such that f−1(ai = g−1(ai) (1 ≦ i ≦ 5), then f ≡ g.

Teichmuller Geometry

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Uniqueness Theorem ◽  
Existence Theorems ◽  
Quadratic Differentials ◽  
Complex Structures ◽  
Metric Geometry ◽  
Quasiconformal Maps ◽  
Hyperbolic Structures ◽  
Teichmüller Metric ◽  
Uniqueness And Existence ◽  
Teichmüller Mapping

This chapter focuses on the metric geometry of Teichmüller space. It first explains how one can think of Teich(Sɡ) as the space of complex structures on Sɡ. To this end, the chapter defines quasiconformal maps between surfaces and presents a solution to the resulting Teichmüller's extremal problem. It also considers the correspondence between complex structures and hyperbolic structures, along with the Teichmüller mapping, Teichmüller metric, and the proof of Teichmüller's uniqueness and existence theorems. The fundamental connection between Teichmüller's theorems, holomorphic quadratic differentials, and measured foliations is discussed as well. Finally, the chapter describes the Grötzsch's problem, whose solution is tied to the proof of Teichmüller's uniqueness theorem.

scholarly journals Havin-Mazya type uniqueness Theorem for Dirichlet spaces

2021 ◽  
pp. 102967
Author(s):  
H. Bahajji-El Idrissi ◽  
O. El-Fallah ◽  
K. Kellay
Keyword(s):  
Uniqueness Theorem ◽  
Dirichlet Spaces

scholarly journals Strong submeasures and applications to non-compact dynamical systems

2020 ◽  
pp. 1-23
Author(s):  
TUYEN TRUNG TRUONG
Keyword(s):  
Metric Space ◽  
Bounded Operator ◽  
Continuous Functions ◽  
Open Dense Subset ◽  
Compact Metric Space ◽  
Basic Properties ◽  
Banach Theorem ◽  
Complex Varieties ◽  
Definition Of ◽  
Meromorphic Maps

Abstract A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreasing. By the Hahn–Banach theorem, a positive strong submeasure is the supremum of a non-empty collection of measures whose masses are uniformly bounded from above. There are many natural examples of continuous maps of the form $f:U\rightarrow X$ , where X is a compact metric space and $U\subset X$ is an open-dense subset, where f cannot extend to a reasonable function on X. We can mention cases such as transcendental maps of $\mathbb {C}$ , meromorphic maps on compact complex varieties, or continuous self-maps $f:U\rightarrow U$ of a dense open subset $U\subset X$ where X is a compact metric space. For the aforementioned mentioned the use of measures is not sufficient to establish the basic properties of ergodic theory, such as the existence of invariant measures or a reasonable definition of measure-theoretic entropy and topological entropy. In this paper we show that strong submeasures can be used to completely resolve the issue and establish these basic properties. In another paper we apply strong submeasures to the intersection of positive closed $(1,1)$ currents on compact Kähler manifolds.

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