This paper proves some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space p^N（C） with truncated multiplicities, and our results improve some earlier work.
This article proves the existence of Julia directions of value distribution of holomorphic mapping f from the unit disk into the n-dimensional complex projective spacePn（C） under the assumption limsupT（r,f）/log 1/...This article proves the existence of Julia directions of value distribution of holomorphic mapping f from the unit disk into the n-dimensional complex projective spacePn（C） under the assumption limsupT（r,f）/log 1/1-r = ＋∞ for hypersurfaces in general position. A heuristic principle concerning the existence of Julia directions of holomorphic mappings from the unit disk into Pn（C） is given also.展开更多
In this paper,a uniqueness theorem for meromorphic mappings partially sharing 2N+3 hyperplanes is proved.For a meromorphic mapping f and a hyperplane H,set E(H,f) = {z|ν(f,H)(z) 】 0}.Let f and g be two linearly non-...In this paper,a uniqueness theorem for meromorphic mappings partially sharing 2N+3 hyperplanes is proved.For a meromorphic mapping f and a hyperplane H,set E(H,f) = {z|ν(f,H)(z) 】 0}.Let f and g be two linearly non-degenerate meromorphic mappings and {Hj}j2=N1+ 3be 2N + 3 hyperplanes in general position such that dim f-1(Hi) ∩ f-1(Hj) n-2 for i = j.Assume that E(Hj,f) E(Hj,g) for each j with 1 j 2N +3 and f = g on j2=N1+ 3f-1(Hj).If liminfr→+∞ 2j=N1+ 3N(1f,Hj)(r) j2=N1+ 3N(1g,Hj)(r) 】 NN+1,then f ≡ g.展开更多
In this article, we prove a degeneracy theorem for three linearly non-degenerate meromorphic mappings from Cn into PN （C）, sharing 2N ＋ 2 hyperplanes in general position, counted with multiplicities truncated by 2.
In this paper, we first establish a truncated Second Main Theorem for algebraically nondegenerate holomorphic mappings from the complex plane into a complex projective variety V intersecting hypersurfaces. We then pro...In this paper, we first establish a truncated Second Main Theorem for algebraically nondegenerate holomorphic mappings from the complex plane into a complex projective variety V intersecting hypersurfaces. We then prove some uniqueness results for meromorphic mappings. The result of Demailly about a partial solution to the Fujita’s conjecture is used.展开更多
Riemann Hypothesis was posed by Riemann in early 50’s of the 19th century in his thesis titled “The Number of Primes less than a Given Number”. It is one of the unsolved “Supper” problems of mathematics. The Riem...Riemann Hypothesis was posed by Riemann in early 50’s of the 19th century in his thesis titled “The Number of Primes less than a Given Number”. It is one of the unsolved “Supper” problems of mathematics. The Riemann Hypothesis is closely related to the well-known Prime Number Theorem. The Riemann Hypothesis states that all the nontrivial zeros of the zeta-function lie on the “critical line” . In this paper, we use Nevanlinna’s Second Main Theorem in the value distribution theory, refute the Riemann Hypothesis. In reference [7], we have already given a proof of refute the Riemann Hypothesis. In this paper, we gave out the second proof, please read the reference.展开更多
Let F be a family of holomorphic curves of a domain D in C into a closed subset X in ■~N(C). Let Q_1(z),…, Q_(2t+1)(z) be moving hypersurfaces in ■~N(C) located in pointwise t-subgeneral position with respect to X....Let F be a family of holomorphic curves of a domain D in C into a closed subset X in ■~N(C). Let Q_1(z),…, Q_(2t+1)(z) be moving hypersurfaces in ■~N(C) located in pointwise t-subgeneral position with respect to X. If each pair of curves f and g in F share the set {Q_1(z),…, Q_(2t+1)(z)}, then F is normal on D. This result greatly extend some earlier theorems related to Montel's criterion.展开更多
基金supported in part by the National Natural Science Foundation of China(10971156,11271291)
文摘This paper proves some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space p^N（C） with truncated multiplicities, and our results improve some earlier work.
基金supported by the National Natural Science Foundation of China(Grant No.10571135)Doctoral Program Foundation of the Ministry of China(Grant No.20050247011).
文摘In this article, some uniqueness theorems of meromorphic mappings are proved.
基金project supported in part by the National Natural Science Foundation of China(10971156)
文摘This article proves the existence of Julia directions of value distribution of holomorphic mapping f from the unit disk into the n-dimensional complex projective spacePn（C） under the assumption limsupT（r,f）/log 1/1-r = ＋∞ for hypersurfaces in general position. A heuristic principle concerning the existence of Julia directions of holomorphic mappings from the unit disk into Pn（C） is given also.
基金supported by National Natural Science Foundation of China (Grant Nos.10871145,10901120)Doctoral Program Foundation of the Ministry of Education of China (Grant No.20090072110053)
文摘In this paper,a uniqueness theorem for meromorphic mappings partially sharing 2N+3 hyperplanes is proved.For a meromorphic mapping f and a hyperplane H,set E(H,f) = {z|ν(f,H)(z) 】 0}.Let f and g be two linearly non-degenerate meromorphic mappings and {Hj}j2=N1+ 3be 2N + 3 hyperplanes in general position such that dim f-1(Hi) ∩ f-1(Hj) n-2 for i = j.Assume that E(Hj,f) E(Hj,g) for each j with 1 j 2N +3 and f = g on j2=N1+ 3f-1(Hj).If liminfr→+∞ 2j=N1+ 3N(1f,Hj)(r) j2=N1+ 3N(1g,Hj)(r) 】 NN+1,then f ≡ g.
基金supported by the National Natural Science Foundation of China(10871145, 10901120)Doctoral Program Foundation of the Ministry of Education of China (20090072110053)
文摘In this article, we prove a degeneracy theorem for three linearly non-degenerate meromorphic mappings from Cn into PN （C）, sharing 2N ＋ 2 hyperplanes in general position, counted with multiplicities truncated by 2.
基金supported in part by NSA grants H98230-07-1-0050 and H98230-09-1-0004supported in part by National Nataral Science Foundation of China(Grant Nos. 10871145 and 10901120)the Doctor Program Foundation of the Ministry of Education of China(Grant No. 20090072110053)
文摘In this paper, we first establish a truncated Second Main Theorem for algebraically nondegenerate holomorphic mappings from the complex plane into a complex projective variety V intersecting hypersurfaces. We then prove some uniqueness results for meromorphic mappings. The result of Demailly about a partial solution to the Fujita’s conjecture is used.
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 11171255, 10901120） and the Doctoral Program Foundation of the Ministry of Education of China （Grant No. 20090072110053）.
文摘In this paper, we give a uniqueness theorem for meromorphic mappings from Cn into P^N（C） with rank ≥ μ regardless of multiplicities.
文摘Riemann Hypothesis was posed by Riemann in early 50’s of the 19th century in his thesis titled “The Number of Primes less than a Given Number”. It is one of the unsolved “Supper” problems of mathematics. The Riemann Hypothesis is closely related to the well-known Prime Number Theorem. The Riemann Hypothesis states that all the nontrivial zeros of the zeta-function lie on the “critical line” . In this paper, we use Nevanlinna’s Second Main Theorem in the value distribution theory, refute the Riemann Hypothesis. In reference [7], we have already given a proof of refute the Riemann Hypothesis. In this paper, we gave out the second proof, please read the reference.
基金The NSF(11701006,11471163) of Chinathe NSF(1808085QA02) of Anhui Province
文摘Let F be a family of holomorphic curves of a domain D in C into a closed subset X in ■~N(C). Let Q_1(z),…, Q_(2t+1)(z) be moving hypersurfaces in ■~N(C) located in pointwise t-subgeneral position with respect to X. If each pair of curves f and g in F share the set {Q_1(z),…, Q_(2t+1)(z)}, then F is normal on D. This result greatly extend some earlier theorems related to Montel's criterion.
