A new version of the second main theorem for meromorphic mappings intersecting hyperplanes in several complex variables
By Ting-Bin Cao, R. Korhonen. 2016
93 citations recorded by the source corpus.
Abstract Let c ∈ C m , f : C m → P n ( C ) be a linearly nondegenerate meromorphic mapping over the field P c of c-periodic meromorphic functions in C m , and let H j ( 1 ≤ j ≤ q ) be q ( > 2 N − n + 1 ) hyperplanes in N-subgeneral position of P n ( C ) . We prove a new version of the second main theorem for meromorphic mappings of hyperorder strictly less than one without truncated multiplicity by considering the Casorati determinant of f instead of its Wronskian determinant. As its applications, we obtain a defect relation, a uniqueness theorem and a difference analogue of generalized Picard theorem.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/988ee59c1b2713efcf87bff9f8cedd664e7100cb
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Logarithmic difference lemma in several complex variables and partial difference equations (2018, background): “By the new version of the logarithmic difference lemma, all the second main theorem and Picard type theorem for meromorphic mappings from C into complex projective spaces P(C) obtained in [29, 3, 4] (including also [20, 43, 30, 5]) can be improved under the assumption of (10).”