In this article, we prove a Picard-type Theorem and a uniqueness theorem for non-Archimedean analytic curves in the projective space Pn(F), where the characteristic of F is 0 or positive. In the main results of this a...In this article, we prove a Picard-type Theorem and a uniqueness theorem for non-Archimedean analytic curves in the projective space Pn(F), where the characteristic of F is 0 or positive. In the main results of this article, we ignore the zeros with large multiplicities.展开更多
Let M be an open Riemann surface and G:M→Pn(C)be a holomorphic map.Consider the conformal metric on M which is given by ds^(2)=‖■‖^(2m)|w|^(2),where■is a reduced representation of G,ωis a holomorphic 1-form on M...Let M be an open Riemann surface and G:M→Pn(C)be a holomorphic map.Consider the conformal metric on M which is given by ds^(2)=‖■‖^(2m)|w|^(2),where■is a reduced representation of G,ωis a holomorphic 1-form on M and m is a positive integer.Assume that ds^(2) is complete and G is k-nondegenerate(0≤k≤n).If there are q hyperplanes H1,H2,…,Hq■Pn(C)located in general position such that G is ramified over Hj with multiplicity at leastγj(>k)for each j∈{1,2,…,q},and it holds that■,then M is flat,or equivalently,G is a constant map.Moreover,one further give a curvature estimate on M without assuming the completeness of the surface.展开更多
The authors introduce a new idea related to Montel-type theorems in higher dimension and prove some Montel-type criteria for normal families of holomorphic mappings and normal holomorphic mappings of several complex v...The authors introduce a new idea related to Montel-type theorems in higher dimension and prove some Montel-type criteria for normal families of holomorphic mappings and normal holomorphic mappings of several complex variables into PN(C) for continuously moving hyperplanes in pointwise general position. The main results are also true for continuously moving hypersurfaces in pointwise general position. Examples are given to show the sharpness of the results.展开更多
Let f（z） be a meromorphic function in the complex plane, whose zeros have multiplicity at least k ＋ 1 （k 〉 2）. If sin z is a small function with respect to f（z）, then f（k） （z） - P（z） sin z has infinitely...Let f（z） be a meromorphic function in the complex plane, whose zeros have multiplicity at least k ＋ 1 （k 〉 2）. If sin z is a small function with respect to f（z）, then f（k） （z） - P（z） sin z has infinitely many zeros in the complex plane, where P（z） is a nonzero polynomial of deg（P（z）） ≠ 1. Keywords Meromorphic function, Nevanlinna theory, Picard type theorem.展开更多
基金supported by Education Department of Henan Province(16A110029)NSFC(11571256)
文摘In this article, we prove a Picard-type Theorem and a uniqueness theorem for non-Archimedean analytic curves in the projective space Pn(F), where the characteristic of F is 0 or positive. In the main results of this article, we ignore the zeros with large multiplicities.
基金supported by the National Natural Science Foundation of China(Nos.12101068,12261106,12171050)。
文摘Let M be an open Riemann surface and G:M→Pn(C)be a holomorphic map.Consider the conformal metric on M which is given by ds^(2)=‖■‖^(2m)|w|^(2),where■is a reduced representation of G,ωis a holomorphic 1-form on M and m is a positive integer.Assume that ds^(2) is complete and G is k-nondegenerate(0≤k≤n).If there are q hyperplanes H1,H2,…,Hq■Pn(C)located in general position such that G is ramified over Hj with multiplicity at leastγj(>k)for each j∈{1,2,…,q},and it holds that■,then M is flat,or equivalently,G is a constant map.Moreover,one further give a curvature estimate on M without assuming the completeness of the surface.
基金Project supported by the National Natural Science Foundation of China (No. 10971156)the Department of Mathematics, HKUST and Fields Institute for kind hospitality and support while part of the work on this paper took place
文摘The authors introduce a new idea related to Montel-type theorems in higher dimension and prove some Montel-type criteria for normal families of holomorphic mappings and normal holomorphic mappings of several complex variables into PN(C) for continuously moving hyperplanes in pointwise general position. The main results are also true for continuously moving hypersurfaces in pointwise general position. Examples are given to show the sharpness of the results.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11301140,11671191 and 11501367)China Postdoctoral Science Foundation(Grant No.2015M571726)the Project of Sichuan Provincial Department of Education(Grant No.15ZB0172)
文摘Let f（z） be a meromorphic function in the complex plane, whose zeros have multiplicity at least k ＋ 1 （k 〉 2）. If sin z is a small function with respect to f（z）, then f（k） （z） - P（z） sin z has infinitely many zeros in the complex plane, where P（z） is a nonzero polynomial of deg（P（z）） ≠ 1. Keywords Meromorphic function, Nevanlinna theory, Picard type theorem.
