scholarly journals A Lehto–Virtanen-type theorem and a rescaling principle for an isolated essential singularity of a holomorphic curve in a complex space

2015 ◽  
Vol 26 (06) ◽  
pp. 1541009
Author(s):  
Yûsuke Okuyama
Keyword(s):  
Complex Space ◽  
Type Theorem ◽  
Essential Singularity ◽  
Holomorphic Curves ◽  
Holomorphic Curve ◽  
Picard Type Theorem

We establish a Lehto–Virtanen-type theorem and a rescaling principle for an isolated essential singularity of a holomorphic curve in a complex space, which are useful for establishing a big Picard-type theorem and a big Brody-type one for holomorphic curves.

scholarly journals On Existence Theorems to Symmetric Functional Set-Valued Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1219
Author(s):  
Marek T. Malinowski
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Existence Theorems ◽  
Type Theorem ◽  
Integral Representations ◽  
Uniqueness Of The Solution ◽  
Nonempty Compact ◽  
Picard Type Theorem ◽  
Convex Subsets

In this paper, we consider functional set-valued differential equations in their integral representations that possess integrals symmetrically on both sides of the equations. The solutions have values that are the nonempty compact and convex subsets. The main results contain a Peano type theorem on the existence of the solution and a Picard type theorem on the existence and uniqueness of the solution to such equations. The proofs are based on sequences of approximations that are constructed with appropriate Hukuhara differences of sets. An estimate of the magnitude of the solution’s values is provided as well. We show the closeness of the unique solutions when the equations differ slightly.

scholarly journals Transverse J-holomorphic curves in nearly Kähler $$\mathbb {CP}^3$$

2021 ◽  
Author(s):  
Benjamin Aslan
Keyword(s):  
Minimal Surfaces ◽  
Type Theorem ◽  
Holomorphic Curves ◽  
Nearly Kähler ◽  
Flat Tori

AbstractJ-holomorphic curves in nearly Kähler $$\mathbb {CP}^3$$ CP 3 are related to minimal surfaces in $$S^4$$ S 4 as well as associative submanifolds in $$\Lambda ^2_-(S^4)$$ Λ - 2 ( S 4 ) . We introduce the class of transverse J-holomorphic curves and establish a Bonnet-type theorem for them. We classify flat tori in $$S^4$$ S 4 and construct moment-type maps from $$\mathbb {CP}^3$$ CP 3 to relate them to the theory of $$\mathrm {U}(1)$$ U ( 1 ) -invariant minimal surfaces on $$S^4$$ S 4 .

scholarly journals Holomorphic mappings into the complex projective space with moving hypersurfaces

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 955-962
Author(s):  
Liu Yang
Keyword(s):  
Projective Space ◽  
Recent Work ◽  
General Position ◽  
Complex Projective Space ◽  
Type Theorem ◽  
Complex Variables ◽  
Holomorphic Mappings ◽  
Several Complex Variables ◽  
Picard Type Theorem ◽  
Complex Projective

Motivated by Eremenko?s accomplisshment of a Picard-type theorem [Period Math Hung. 38 (1999), pp.39-42.], we study the normality of families of holomorphic mappings of several complex variables into PN(C) for moving hypersurfaces located in general position. Our results generalize and complete previous results in this area, especially the works of Dufresnoy, Tu-Li, Tu-Cao, Yang-Fang-Pang and the recent work of Ye-Shi-Pang.

scholarly journals A Picard type theorem concerning meromorphic functions of\\ hyper-order

2016 ◽  
Vol 47 (3) ◽  
pp. 357-370 ◽  
Author(s):  
PANG XueCheng ◽  
YANG Pai ◽  
NIU PeiYan
Keyword(s):  
Meromorphic Functions ◽  
Type Theorem ◽  
Hyper Order ◽  
Picard Type Theorem

scholarly journals A new Picard type theorem concerning elliptic functions

2015 ◽  
Vol 40 ◽  
pp. 17-30
Author(s):  
Qiaoyu Chen ◽  
Xuecheng Pang ◽  
Pai Yang
Keyword(s):  
Type Theorem ◽  
Elliptic Functions ◽  
Picard Type Theorem
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