A note on the uniqueness theorem of meromorphic mappings

In this article, some uniqueness theorems of meromorphic mappings are proved.     

Uniqueness problem for meromorphic mappings in several complex variables with few hyperplanes

The purpose of this article is to deal with uniqueness problem with truncated multiplicities for meromorphic mappings in several complex variables. We obtain a degeneracy theorem of meromorphic mappings without taking account of multiplicities of order k in counting functions and a uniqueness theorem for meromorphic mappings sharing 2n + 2(n ≥ 2) hyperplanes in general position, which improve and extend some earlier work.     

Uniqueness theorems for meromorphic mappings with few hyperplanes

Let f,g be linearly nondegenerate meromorphic mappings of Cm into CPn. Let be hyperplanes in CPn in general position, such that

(a)

f−1(Hj)=g−1(Hj), for all 1?j?q,

(b)

dim(f−1(Hi)∩f−1(Hj))?m−2 for all 1?i<j?q, and

(c)

f=g on .

It is well known that if q?3n+2, then f≡g. In this paper we show that for every nonnegative integer c there exists positive integer N(c) depending only on c in an explicit way such that the above result remains valid if q?(3n+2−c) and n?N(c). Furthermore, we also show that the coefficient of n in the formula of q can be replaced by a number which is strictly smaller than 3 for all n?0. At the same time, a big number of recent uniqueness theorems are generalized considerably.     

A uniqueness theorem for meromorphic mappings in several complex variables

In this paper, we give a uniqueness theorem for meromorphic mappings from ?n into ?N(?) with rank≥μregardless of multiplicities.     

分担处于一般位置超平面的亚纯映射唯一性定理

本文研究从Cn到复射影空间PN(C)上亚纯映射唯一性问题.根据杨乐处理重值的方法和Dethloff、Quang、Tan等人的技巧,我们分别得到了两个广泛的唯一性定理,改进和推广了一些分担处于一般位置超平面的亚纯映射唯一性结果.     

A note on uniqueness for the plasma problem

Summary We prove uniqueness for the plasma problem for certain symmetric domains. We also obtain a number of counterexamples where there is non-uniqueness and where there are sometimes secondary bifurcations.Dedicated to Klaus Kirchgässner on the occasion of his sixtieth birthdayI should like to thank G. Keady for some useful conversations.     

Non-integrated defect relation for meromorphic mappings on Kähler manifolds intersecting non-subdegenerate families of hyperplanes

Let M be a complete Kähler manifold, whose universal covering is biholomorphic to a ball ${\mathbb{B}}^m(R_0)$ in ${\mathbb{C}}^m$ ($0<R_0\le +\infty$). Our purpose of this article is to establish a non-integrated defect relation with truncated level for a meromorphic mapping on M intersecting a family of hyperplanes in ${\mathbb{P}}^n(\mathbb{C})$ which is non-subdegenerate with respect to the mapping.     

A degeneracy theorem for meromorphic mappings with truncated multiplicities

In this article, we prove a degeneracy theorem for three linearly non-degenerate meromorphic mappings from C n into P N (C), sharing 2N + 2 hyperplanes in general position, counted with multiplicities truncated by 2.     

A note on meromorphic convexity

We give examples of Stein domains D in C ² such that C ² ? D is either completely pluripolar or union of germs of (principal) hypersurfaces not intersecting D such that D fails to be meromorphically convex in C ². © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

A note on the uniqueness problem of non-Archimedean holomorphic curves

We prove a uniqueness theorem for non-Archimedean linearly nondegenerate holomorphic curves in projective spaces of dimension $n$ with two families of $(2n+2)$ hyperplanes in general position. Our result strongly generalizes the uniqueness theorem with $(3n+1)$ hyperplanes of Ru in [11].     

A note on meromorphic operators

Let be a complex Banach space and a bounded linear operator on . is called meromorphic if the spectrum of is a countable set, with the only possible point of accumulation, such that all the nonzero points of are poles of . By means of the analytical core we give a spectral theory of meromorphic operators. Our results are a generalization of some results obtained by Gong and Wang (2003).

     

A note on sequence-covering mappings

Summary Let f: X &rarr; Y be a mapping. f is called a sequence-covering mapping if in case S is a convergent sequence containing its limit point in Y then there is a compact subset K of X such that f(K) = S. It is shown that each quotient and compact mapping of a metric space is sequence-covering.     

A note on existence, uniqueness and continuous dependence for a non-linear heat conduction problem

^** Email: cimatti{at}dm.unipi.it Using the Levy–Caccioppoli global inversion theorem, aresult of existence, uniqueness and continuous dependence isproved for a non-linear problem of heat conduction.