A Defect Relation for Quasimeromorphic Mappings

1981 ◽  
Vol 114 (1) ◽  
pp. 165 ◽  
Author(s):  
Seppo Rickman
Keyword(s):  
Defect Relation ◽  
Quasimeromorphic Mappings

scholarly journals On value distributions for quasimeromorphic mappings on H-type Carnot groups

2006 ◽  
Vol 130 (6) ◽  
pp. 467-523 ◽  
Author(s):  
Irina Markina ◽  
Sergey Vodopyanov
Keyword(s):  
Carnot Groups ◽  
Quasimeromorphic Mappings

scholarly journals Lindelöf's theorem for normal quasimeromorphic mappings.

1990 ◽  
Vol 37 (2) ◽  
pp. 219-226 ◽  
Author(s):  
Juha Heinonen ◽  
John Rossi
Keyword(s):  
Quasimeromorphic Mappings

scholarly journals Modified defect relations for the gauss map of minimal surfaces, III

1991 ◽  
Vol 124 ◽  
pp. 13-40 ◽  
Author(s):  
Hirotaka Fujimoto
Keyword(s):  
Minimal Surface ◽  
Complex Projective Space ◽  
Meromorphic Functions ◽  
Total Curvature ◽  
Gauss Map ◽  
Holomorphic Maps ◽  
Complete Minimal Surface ◽  
Defect Relation ◽  
Definition Of ◽  
Complex Projective

In [5], the author proved that the Gauss map of a nonflat complete minimal surface immersed in R3 can omit at most four points of the sphere, and in [7] he revealed some relations between this result and the defect relation in Nevanlinna theory on value distribution of meromorphic functions. Afterwards, Mo and Osserman obtained an improvement of these results in their paper [11], which asserts that if the Gauss map of a nonflat complete minimal surface M immersed in R3 takes on five distinct values only a finite number of times, then M has finite total curvature. The author also gave modified defect relations for holomorphic maps of a Riemann surface with a complete conformai metric into the n-dimensional complex projective space Pn(C) and, as its application, he showed that, if the (generalized) Gauss map G of a complete minimal surface M immersed in Rm is nondegenerate, namely, the image G(M) is not contained in any hyperplane in Pm − 1(C), then it can omit at most m(m + 1)/2 hyperplanes in general position ([8]). Here, the number m(m + 1)/2 is best-possible for arbitrary odd numbers and some small even numbers m (see [6]). Recently, Ru showed that the “nondegenerate” assumption of the above result can be dropped ([13]). In this paper, we shall introduce a new definition of modified defect and prove a refined Modified defect relation. As its application, we shall give some improvements of the above-mentioned results in [5], [7], [8], [11] and [13].

QUASIMEROMORPHIC MAPPINGS OF SEVERAL COMPLEX VARIABLES

1999 ◽  
Vol 19 (5) ◽  
pp. 541-547 ◽  
Author(s):  
Zehua Zhou ◽  
Daochun Sun
Keyword(s):  
Complex Variables ◽  
Several Complex Variables ◽  
Quasimeromorphic Mappings

An analogue of the defect relation for the uniform metric, II

1998 ◽  
Vol 37 (1-4) ◽  
pp. 145-159
Author(s):  
A. Eremenko
Keyword(s):  
Defect Relation
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