共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
Emmanuel Preissmann 《Monatshefte für Mathematik》2007,45(1):233-239
Let X
0 be the germ at 0 of a complex variety and let
f: X0? \Bbb Cn0f:\ X_0\rightarrow {\Bbb C}^n_0
be a holomorphic germ. We say that f is pseudoimmersive if for any
g: \Bbb R0? X0g:\ {\Bbb R}_0\rightarrow X_0
such that
f °g ? C¥ f \circ g \in C^{\infty}
, we have
g ? C¥g\in C^{\infty}
. We prove that f is pseudoimmersive if and only if it is injective. Some results about the real case are also considered. 相似文献
3.
Emmanuel Preissmann 《Monatshefte für Mathematik》2007,150(3):233-239
Let X
0 be the germ at 0 of a complex variety and let
be a holomorphic germ. We say that f is pseudoimmersive if for any
such that
, we have
. We prove that f is pseudoimmersive if and only if it is injective. Some results about the real case are also considered. 相似文献
4.
Anastasia Frolova Marina Levenshtein David Shoikhet Alexander Vasil’ev 《Complex Analysis and Operator Theory》2014,8(5):1129-1149
We establish some estimates of the angular derivatives from below for holomorphic self-maps of the unit disk ${\mathbb {D}}$ at one and two fixed points of the unit circle provided there is no fixed point inside ${\mathbb {D}}$ . The results complement Cowen–Pommerenke and Anderson–Vasil’ev type estimates in the case of univalent functions. We use the method of extremal length and a semigroup approach to deriving inequalities for holomorphic self-maps of the disk which are not necessarily univalent using known inequalities for univalent functions. This approach allowed us to obtain a new Ossermans type estimate as well as inequalities for holomorphic self-maps which images do not separate the origin and the boundary. 相似文献
5.
§ 1. NotationsandFormulas Let(N ,dS2 N)beaHermitianmanifoldofdimensionn ,anddS2 NitsHermitianmertric.Let{e1~ ,Λen~}oftype (1 ,0 )tangentvectorsconstitutealocalunitaryframefieldinanopensetofM .Let{ω1 ,Λωn}betheunitarycoframewhichconsistsofncomplex valuedlineardifferen tialformsoftype (1 ,0 )suchthatdS2 N =ωαω-α. (1 )Hereandbelowthesummationconventionisused ,i.e .,therepeatedindexmeanssummation .LetBbethebundleofallunitaryframesofN .Thentheforms{ωα}areformsinB .Itiswellkn… 相似文献
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7.
Kazumi Tsukada 《Geometriae Dedicata》1997,68(1):61-71
We investigate holomorphic maps between compact generalized Hopf manifolds (i.e., locally conformal Kähler manifolds with parallel Lee form). We show that they preserve the canonical foliations. Moreover, we study compact complex submanifolds of g.H. manifolds and holomorphic submersions from compact g.H. manifolds. 相似文献
8.
Ding Xieping 《数学年刊B辑(英文版)》1982,3(5):631-638
In this paper we obtain several new results on Common fixed point of commuting maps in L-space and metric space by introducing new contractive type conditions.
Our main results are the following:
Theorem 2. Let f, g be continuous self-mappings of a separated L-space (X, \rightarrow) which is d-complete for some semi-metric d on X. Then f and g have a common fixed point in X if and only if there exist continuous mappings T_1: X\rightarrow g^t_2(X) and $T_2:X\rightarrow f^t_1(X)$ such that $T_1f=fT_1,T_2g=gT_2$ and for all x,y \in X
$d(T_1^px,T_2^py)\leq \Phi(d(f^t_1x,g^t_2y),d(f^t_1,T_1^px),d(g^t_2y,T_2^qy)),$ where t_1, t_2, p, q\in N and $\Phi:R__^3 \rightarrow R_+$ which is nondecreasing in each coordinate variable and satisfy $\phi(t)=\Phi(t,t,t),\sum\limits_{n=1}^\infty(\phi^n(t)<\infty,\forall t>0$, . Indeed,each of pairs (T_1,f(and (T_2, g)have a u-nique common fixed point and these two points coincide.
Theorem 3. Let f, g be continuous self-mappings of a L-spaces (X, \rightarrow), T_1, T_2 be any self-mappings of X such that T_1(X)\subset g^t_2(X), T_2(X)\subset f^t_2(X),T_1f=fT_1,T_2g=gT_2,where t_1,t_2\in N.suppose(X,\rightarrow) is d-complete for some continuous demi-metric d.If there exist p,q\in N and the function \Phi:R_+^3\rightarrow R_+ Satisfying the supposition in Theorem 2 such that for all x,y \in X
$d(Ux,Vy)\leq \Phi(d(Sx,Ry),d(Sx,Ux),d(Ry,Vy))$
where U-T_1^p,V-T_2^\alpha,S=f^t_1 and R=g^t_2.Then each of pairs (T_1,f) and (T_2,g) have a unique common fixed point and these two points coincide.
Theorem 5. Let f, g be self-mappings of a complete metric space (X, d). For
some fixed m, k\in N, f^m and g^k are continuous, suppose {T_n}_{n\in N} a sequence of selfmappings of X such that T_n( f^m-l (X) \cap g^k-1(X)) \subset f(f^m-1(X) \cap g^k-1(X))\capg(f^m-1(X)\\cap g^k-1(X)),T_nf=fT_n,T_ng-gT_n,\forall n \in N.
If there exist an upper semi-continuous function \Phi:R_+4\rightarrowR_+ which is nondecreasing in oo each coordinate variable such that \phi(t)=\phi(t,t,t,t) satisfies \sum\limits_{n=0}^\infty \phi^n(t)<\infty,\forall t>0 and such that for all x, y\in X ,
i, j\in N,i \ne j,
d(T_ix, T_jy)\leq\Phi(d(fx, gy), d(fx, T_ix), d(gy, T_jy),
1/2[ d(fx, T_jy) +d(gy, T_ix)] .
Then each of pairs ({T_n}n\in N,f) and ({T_n}_n\in N,g) have a unique common fixed point
and these two points ooinoide.
some important rCT’^a of [3—8, 10, 11] are the speoial cases of our results. 相似文献
9.
Let R be a semiprime ring with symmetric Martindale quotient ring Q, n ≥ 2 and let f(X) = X n h(X), where h(X) is a polynomial over the ring of integers with h(0) = ±1. Then there is a ring decomposition Q = Q 1 ⊕ Q 2 ⊕ Q 3 such that Q 1 is a ring satisfying S 2n?2, the standard identity of degree 2n ? 2, Q 2 ? M n (E) for some commutative regular self-injective ring E such that, for some fixed q > 1, x q = x for all x ∈ E, and Q 3 is a both faithful S 2n?2-free and faithful f-free ring. Applying the theorem, we characterize m-power commuting maps, which are defined by linear generalized differential polynomials, on a semiprime ring. 相似文献
10.
Willian Franca 《代数通讯》2013,41(6):2621-2634
Let R be a simple unital ring. Under a mild technical restriction on R, we will characterize biadditive mappings G: R2 → R satisfying G(u, u)u = uG(u, u), and G(1, r) = G(r, 1) = r for all unit u ∈ R and r ∈ R, respectively. As an application, we describe bijective linear maps θ: R → R satisfying θ(xyx?1y?1) = θ(x)θ(y)θ(x)?1θ(y)?1 for all invertible x, y ∈ R. This solves an open problem of Herstein on multiplicative commutators. More precisely, we will show that θ is an isomorphism. Furthermore, we shall see the existence of a unital simple ring R′ without nontrivial idempotents, that admits a bijective linear map f: R′ → R′, preserving multiplicative commutators, that is not an isomorphism. 相似文献
11.
对满足一定条件的非光滑有界域上的全纯逆紧映射证得了局部全纯延拓定理. 同时也研究了广义Hartogs三角形之间的全纯逆紧映射. 相似文献
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Min Ho Lee 《Monatshefte für Mathematik》2004,141(3):187-196
Let
be an equivariant holomorphic map of symmetric domains associated to a homomorphism
of semisimple algebraic groups defined over
. If
and
are torsion-free arithmetic subgroups with
, the map induces a morphism :
of arithmetic varieties and the rationality of is defined by using symmetries on
and
as well as the commensurability groups of and . An element
determines a conjugate equivariant holomorphic map
of which induces the conjugate morphism
of . We prove that is rational if is rational. 相似文献
14.
Min Ho Lee 《Monatshefte für Mathematik》2004,78(4):187-196
Let
t: D ?D¢\tau: {\cal D} \rightarrow{\cal D}^\prime
be an equivariant holomorphic map of symmetric domains associated to a homomorphism
r: \Bbb G ?\Bbb G¢{\bf\rho}: {\Bbb G} \rightarrow{\Bbb G}^\prime
of semisimple algebraic groups defined over
\Bbb Q{\Bbb Q}
. If
G ì \Bbb G (\Bbb Q)\Gamma\subset {\Bbb G} ({\Bbb Q})
and
G¢ ì \Bbb G¢(\Bbb Q)\Gamma^\prime \subset {\Bbb G}^\prime ({\Bbb Q})
are torsion-free arithmetic subgroups with
r (G) ì G¢{\bf\rho} (\Gamma) \subset \Gamma^\prime
, the map G\D ?G¢\D¢\Gamma\backslash {\cal D} \rightarrow\Gamma^\prime \backslash {\cal D}^\prime
of arithmetic varieties and the rationality of D{\cal D}
and
D¢{\cal D}^\prime
as well as the commensurability groups of
s ? Aut (\Bbb C)\sigma \in {\rm Aut} ({\Bbb C})
determines a conjugate equivariant holomorphic map
ts: Ds ?D¢s\tau^\sigma: {\cal D}^\sigma \rightarrow{\cal D}^{\prime\sigma}
of fs: (G\D)s ?(G¢\D¢)s\phi^\sigma: (\Gamma\backslash {\cal D})^\sigma \rightarrow(\Gamma^\prime \backslash {\cal D}^\prime)^\sigma
of . We prove that is rational if is rational. 相似文献
15.
《数学的实践与认识》2017,(18)
设N是维数大于2的复可分Hilbert空间H上的套且τ(N)是相应的套代数.利用Peirce分解的方法证明了:Φ是τ(N)上的一个映射(没有线性的假设),对任意的A,B∈τ(N),如果满足等式[A,Φ(B)]=[Φ(A),B]那么存在映射f:τ(N)→CI及α∈C,有Φ(A)=αA+f(A). 相似文献
16.
Itiswell-knownthattheanalyticfunctionwithpositiverealpartintheunitdiscofthecomplexplaneplaysaveryimportantroleinthegeometrictheoryofcomplexvariablefunc-tions.Ithasbeenremarkablehowtoextendtheclassicalresultofthetheoryoffunctionstoabstractspacesinrecentyears[2].Inthisnotewedefineageneralizedhalf-planeinHilbertspaceandfindthebiholomorphicmapoftheunitballonHilbertspaceontothishalf-plane.Asacorollary,wegiveashortproofofaresultin[5].UsingtheaboveholomooorphicmapweobtainthedistortiontheoremandPick… 相似文献
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18.
We study the dynamics of commuting rational maps with coefficients in Cp. By lifting the dynamics from P1(Cp) to Berkovich projective space P1 Berk, we prove that two nonlinear commuting maps have the same Berkovich Julia set and the same canonical measure. As a consequence, two nonlinear commuting maps with coefficient in Cp have the same classical Julia set. We also prove that they have the same pre-periodic Berkovich Fatou components. 相似文献
19.
We prove that a proper holomorphic map on the unit disk in thecomplex plane is uniquely determined up to post-compositionwith a Möbius transformation by its critical points. 1991Mathematics Subject Classification 30C99, 30F45. 相似文献
20.
Ngaiming MOK 《数学年刊B辑(英文版)》2008,29(2):135-146
The author,motivated by his results on Hermitian metric rigidity,conjectured in [4] that a proper holomorphic mapping f:Ω→Ω′from an irreducible bounded symmetric domainΩof rank≥2 into a bounded symmetric domainΩ′is necessarily totally geodesic provided that r′:=rank(Ω′)≤rank(Ω):=r.The Conjecture was resolved in the affirmative by I.-H.Tsai [8].When the hypothesis r′≤r is removed,the structure of proper holomorphic maps f:Ω→Ω′is far from being understood,and the complexity in studying such maps depends very much on the difference r′-r,which is called the rank defect.The only known nontrivial non-equidimensional structure theorems on proper holomorphic maps are due to Z.-H.Tu [10],in which a rigidity theorem was proven for certain pairs of classical domains of type I,which implies nonexistence theorems for other pairs of such domains.For both results the rank defect is equal to 1,and a generaliza- tion of the rigidity result to cases of higher rank defects along the line of arguments of [10] has so far been inaccessible. In this article, the author produces nonexistence results for infinite series of pairs of (Ω→Ω′) of irreducible bounded symmetric domains of type I in which the rank defect is an arbitrarily prescribed positive integer. Such nonexistence results are obtained by exploiting the geometry of characteristic symmetric subspaces as introduced by N. Mok and L-H Tsai [6] and more generally invariantly geodesic subspaces as formalized in [8]. Our nonexistence results motivate the formulation of questions on proper holomorphic maps in the non-equirank case. 相似文献