The ahlfors — Weyl theory of meromorphic maps on parabolic manifolds

1983 ◽  
pp. 101-219 ◽  
Author(s):  
Wilhelm Stoll
Keyword(s):  
Weyl Theory ◽  
Meromorphic Maps

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.

scholarly journals Conformal measures for meromorphic maps

2018 ◽  
Vol 43 ◽  
pp. 247-266
Author(s):  
Krzysztof Baranski ◽  
Boguslawa Karpinska ◽  
Anna Zdunik
Keyword(s):  
Conformal Measures ◽  
Meromorphic Maps

scholarly journals Dynamics of meromorphic maps with small topological degree I: from cohomology to currents

2010 ◽  
Vol 59 (2) ◽  
pp. 521-562 ◽  
Author(s):  
Jeffrey Diller ◽  
Romain Dujardin ◽  
Vincent Guedj
Keyword(s):  
Topological Degree ◽  
Meromorphic Maps

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

1975 ◽  
Vol 83 ◽  
pp. 153-181 ◽  
Author(s):  
Hirotaka Fujimoto
Keyword(s):  
General Position ◽  
Uniqueness Problem ◽  
Meromorphic Maps

Let H1, H2, …, HN+2 be hyperplanes in PN(C) located in general position and v1v2, … νN+2 divisors on Cn. We consider the set ℱ(Hi, νi) of all non-degenerate meromorphic maps of Cn into PN(C) such that the pull-backs ν(f, Hi) of the divisors (Hi) on PN(C) by f are equal to νi for any i = 1, 2, …, N + 2. In the previous paper [6], the author showed that =:= ℱ(Hi, νi) cannot contain more than N+ 1 algebraically independent maps. Relating to this, the following theorem will be proved.

scholarly journals Equidistribution for meromorphic maps with dominant topological degree

2015 ◽  
Vol 64 (6) ◽  
pp. 1805-1828 ◽  
Author(s):  
Tien-Cuong Dinh ◽  
Viet anh Nguyen ◽  
Tuyen Trung Truong
Keyword(s):  
Topological Degree ◽  
Meromorphic Maps
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