Second Main Theorem of Nevalinna Theory for Nonequidimensional Meromorphic Maps

1994 ◽  
Vol 116 (5) ◽  
pp. 1031 ◽  
Author(s):  
Pit-Mann Wong ◽  
Wilhelm Stoll
Keyword(s):  
Second Main Theorem ◽  
Meromorphic Maps

scholarly journals Algebro-geometric version of Nevanlinna’s lemma on logarithmic derivative and applications

2004 ◽  
Vol 173 ◽  
pp. 23-63 ◽  
Author(s):  
Katsutoshi Yamanoi
Keyword(s):  
Nevanlinna Theory ◽  
Affine Space ◽  
Projective Variety ◽  
Logarithmic Derivative ◽  
Second Main Theorem ◽  
Smooth Complex ◽  
Complex Projective Variety ◽  
Meromorphic Maps ◽  
Complex Projective ◽  
The Second Main Theorem

AbstractIn this paper we shall establish some generalization of Nevanlinna’s Lemma on Logarithmic Derivative to the case of meromorphic maps from a finite analytic covering space over the m-dimensional complex affine space ℂm to a smooth complex projective variety. Then we shall apply this to “the Second Main Theorem” in Nevanlinna theory in several complex variables.

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 On Brauer's second main theorem

1965 ◽  
Vol 2 (3) ◽  
pp. 299-311 ◽  
Author(s):  
E.C Dade
Keyword(s):  
Second Main Theorem
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