共查询到20条相似文献,搜索用时 31 毫秒
1.
D. J. Needham 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,39(3):1092-1095
We give an elementary proof that, in its domain of definition, the time-p map of a scalar, autonomous holomorphic, complex differential equation, is itself holomorphic. This result is used by Sverdlove
[1] when considering limit cycles in complex holomorphic differential equations. However no proof or reference for the result
is given in [1]. Although this result must be well established, a proof does not appear to be readily accessible in the reference
literature. 相似文献
2.
Zhou Xiangyu 《数学学报(英文版)》1993,9(3):261-264
In this note, we'll establish the following Main Theorem. LetD be a locally finite intersection of bounded strictly pseudoconvex domains in a complex space. Then there exists a proper
holomorphic mappingf fromD into some unit ball.
This result is stronger than Grauert-Narasimhan's solution to Levi problem. Our proof is based on a theorem in [10], and other
known results. This note may be regarded as a continuation of [10]. Prof. H. Grauert told me that the present result was an
open problem before we prove it. 相似文献
3.
Roman Lávička 《Advances in Applied Clifford Algebras》2007,17(3):549-554
In [7], B. Fuglede has proved that finely holomorphic functions on a finely open subset U of the complex plane C are finely locally extendable to usual continuously differentiable functions. We shall adopt B. Fuglede’s approach to show
that the same remains true even for functions which have only finely continuous fine differential on U. In higher dimensions, an analogous result may be obtained and the result can be applied to finely monogenic functions which
were introduced recently as a higher dimensional analogue of finely holomorphic functions.
I acknowledge the financial support from the grant GA 201/05/2117. This work is also a part of the research plan MSM 0021620839,
which is financed by the Ministry of Education of the Czech Republic. 相似文献
4.
Radó’s theorem for holomorphic functions asserts that if a continuous function is holomorphic on the complement of its zero
locus, then it is holomorphic everywhere. We prove in this paper an equivalent theorem for functions lying in the kernel of
a first order differential operator D{\mathcal{D}} such that the Helmholtz operator ∇2+λ can be factorized as the composition [^(D)]D{\widehat{\mathcal{D}}\mathcal{D}} . We also analyse the factorisations [^(D)]D{\widehat{\mathcal{D}}\mathcal{D}} of the Laplace and Helmholtz operators associated to the Clifford analysis and the representations of holomorphic function
of several complex variables. 相似文献
5.
The paper deals with a non–linear singular partial differential equation in the holomorphic category. When (E) is of Fuchsian type, the existence of the unique holomorphic solution was established by Gérard –Tahara [2]. In this paper, under the assumption that (E) is of totally characteristic type, the authors give a sufficient condition for (E) to have a unique holomorphic solution. The result is extended to higher order case. 相似文献
6.
N. Blažić M. Prvanović 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2001,71(1):35-47
Let(M, g, J) be an almost Hermitian manifold. In this paper we study holomorphically nonnegatively(δ,Δ)-pinched almost Hermitian manifolds. In [3] it was shown that for such Kahler manifolds a plane with maximal sectional curvature
has to be a holomorphic plane(J-invariant). Here we generalize this result to arbitrary almost Hermitian manifolds with respect to the holomorphic curvature
tensorH R and toRK-manifolds of a constant type λ(p). In the proof some estimates of the sectional curvature are established. The results obtained are used to characterize almost
Hermitian manifolds of constant holomorphic sectional curvature (with respect to holomorphic and Riemannian curvature tensor)
in terms of the eigenvalues of the Jacobi-type operators, i.e. to establish partial cases of the Osserman conjecture. Some
examples are studied.
The first author is partially supported by SFS, Project #04M03. 相似文献
7.
Raffaele Marigo 《Israel Journal of Mathematics》2010,178(1):107-112
The main step in the proof of Hartogs’ theorem on separate analyticity (see [3], [4], [5]) consists in showing that if a function f defined in Δ × Δ is holomorphic for |z
2| < ε and separately holomorphic in z
2 when z
1 is kept fixed, then it is jointly holomorphic; the normal convergence of the Taylor series of f is obtained through the celebrated Hartogs’ lemma on subharmonic functions. 相似文献
8.
We prove that every continuous map from a Stein manifold X to a complex manifold Y can be made holomorphic by a homotopic deformation of both the map and the Stein structure on X. In the absence of topological obstructions, the holomorphic map may be chosen to have pointwise maximal rank. The analogous
result holds for any compact Hausdorff family of maps, but it fails in general for a noncompact family. Our main results are
actually proved for smooth almost complex source manifolds (X,J) with the correct handlebody structure. The paper contains another proof of Eliashberg’s (Int J Math 1:29–46, 1990) homotopy
characterization of Stein manifolds and a slightly different explanation of the construction of exotic Stein surfaces due
to Gompf (Ann Math 148(2): 619–693, 1998; J Symplectic Geom 3:565–587, 2005).
相似文献
9.
《复变函数与椭圆型方程》2012,57(2):167-176
We prove in this paper that, given a nonempty open set G in the complex plane, a subset A of G which is not relatively compact and a holomorphic infinite order differential or antidiffeärential operator T, then there are holomorphic functions ? on G such that the image of A under T ? is dense in the complex plane. This extends a recent result about a property of boundary behaviour exhibited by the derivative operator. 相似文献
10.
Tadej Starčič 《Journal of Geometric Analysis》2008,18(4):1133-1158
In this paper we construct a Stein neighborhood basis for any compact subvariety A with strongly pseudoconvex boundary bA and Stein interior A
\
bA in a complex space X. This is an extension of a well known theorem of Siu. When A is a complex curve, our result coincides with the result proved by Drinovec-Drnovšek and Forstnerič. We shall adapt their
proof to the higher dimensional case, using also some ideas of Demailly’s proof of Siu’s theorem. For embedded strongly pseudoconvex
domain in a complex manifold we also find a basis of tubular Stein neighborhoods. These results are applied to the approximation
problem for holomorphic mappings.
Research supported by grants ARRS (3311-03-831049), Republic of Slovenia. 相似文献
11.
Building on [BB1] we prove a general criterion for convergence of (possibly singular) Bergman measures towards pluripotential-theoretic
equilibrium measures on complex manifolds. The criterion may be formulated in terms of the growth properties of the unit-balls
of certain norms on holomorphic sections, or equivalently as an asymptotic minimization property for generalized Donaldson
L-functionals. Our result settles in particular a well-known conjecture in pluripotential theory concerning the equidistribution
of Fekete points and it gives the convergence of Bergman measures towards the equilibrium measure for Bernstein-Markov measures.
Applications to interpolation of holomorphic sections are also discussed. 相似文献
12.
Michael Wolf 《Journal d'Analyse Mathématique》1996,68(1):107-120
We give a brief, elementary and analytic proof of the theorem of Hubbard and Masur [HM] (see also [K], [G]) that every class
of measured foliations on a compact Riemann surfaceR of genusg can be uniquely represented by the vertical measured foliation of a holomorphic quadratic differential onR. The theorem of Thurston [Th] that the space of classes of projective measured foliations is a 6g—7 dimensional sphere follows immediately by Riemann-Roch. Our argument involves relating each representative of a class of
measured foliations to an equivariant map from
to anR-tree, and then finding an energy minimizing such map by the direct method in the calculus of variations. The normalized Hopf
differential of this harmonic map is then the desired differential.
Partially supported by NSF grant DMS9300001; Alfred P. Sloan Research Fellow. 相似文献
13.
Adam Harris 《Studies in Applied Mathematics》1998,101(3):309-319
The main result of this note treats the problem of unique extension of holomorphic gauge fields across closed subsets of complex Euclidean space, and is based on a corresponding extension theorem for holomorphic vector bundles due to N. P. Buchdahl and the author. Alternatively, let F be a unitary gauge field corresponding to a complex differential form of type (1, 1) (e.g., an anti self-dual Yang–Mills field on a punctured ball in C 2). As a corollary of the main theorem, it is seen that a unique extension of such F , which preserves the curvature type, is obtained if the contraction of F with a holomorphic vector field lies in the image of the ?¯-operator of the associated holomorphic vector bundle. 相似文献
14.
Georg Schneider 《Mathematische Nachrichten》2009,282(1):99-103
In this paper we investigate Hankel operators with anti‐holomorphic L2‐symbols on generalized Fock spaces Am2 in one complex dimension. The investigation of the mentioned operators was started in [4] and [3]. Here, we show that a Hankel operator with anti‐holomorphic L2‐symbol is in the Schatten‐class Sp if and only if the symbol is a polynomial with degree N satisfying 2N < m and p > . The result has been proved independently before in the recent work [2], which also considers the case of several complex variables. However, in addition to providing a different proof for the result the present work shows that the methodology developed in [4] and [3] can be adopted in order to work to characterize Schatten‐class membership. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
Luca Baracco 《Journal of Mathematical Analysis and Applications》2012,388(2):760-762
Real analytic functions on the boundary of the sphere which have separate holomorphic extension along the complex lines through a boundary point have holomorphic extension to the ball. This was proved in Baracco (2009) [4] by an argument of CR geometry. We give here an elementary proof based on the expansion in holomorphic and antiholomorphic powers. 相似文献
16.
For any algebraic super-manifold M we define the super-ind-scheme LM of formal loops and study the transgression map (Radon transform) on differential forms in this context. Applying this to the super-manifold M=SX, the spectrum of the de Rham complex of a manifold X, we obtain, in particular, that the transgression map for X is a quasi-isomorphism between the [2,3)-truncated de Rham complex of X and the additive part of the [1,2)-truncated de Rham complex of LX. The proof uses the super-manifold SSX and the action of the Lie super-algebra sl(1|2) on this manifold. This quasi-isomorphism result provides a crucial step in the classification of sheaves of chiral differential operators in terms of geometry of the formal loop space. 相似文献
17.
Let G be a compact Lie group acting on a compact complex manifold M by holomorphic transformations. We prove a trace density formula for the G-Lefschetz number of a holomorphic differential operator on M. We generalize the recent results of Engeli and the first author to orbifolds. 相似文献
18.
Gheorghe Munteanu 《Periodica Mathematica Hungarica》2007,55(1):97-112
In [Mu1] we underlined the motifs of holomorphic subspaces in a complex Finsler space: induced nonlinear connection, coupling
connections, and the induced tangent and normal connections. In the present paper we investigate the equations of Gauss, H-and A-Codazzi, and Ricci equations of a holomorphic subspace. We deduce the link between the holomorphic curvatures of the Chern-Finsler
connection and its induced tangent connection. Conditions for totally geodesic holomorphic subspaces are obtained.
Communicated by János Szenthe 相似文献
19.
Ngaiming Mok 《中国科学A辑(英文版)》2008,51(4):660-684
In 1993,Tsal proved 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,proving a conjecture of the author's motivated by Hermitian metric rigidity.As a first step in the proof,Tsai showed that df preserves almost everywhere the set of tangent vectors of rank 1.Identifying bounded symmetric domains as open subsets of their compact duals by means of the Borel embedding,this means that the germ of f at a general point preserves the varieties of minimal rational tangents(VMRTs). In another completely different direction Hwang-Mok established with very few exceptions the Cartan- Fubini extension priniciple for germs of local biholomorphisms between Fano manifolds of Picard num- ber 1,showing that the germ of map extends to a global biholomorphism provided that it preserves VMRTs.We propose to isolate the problem of characterization of special holomorphic embeddings between Fano manifolds of Picard number 1,especially in the case of classical manifolds such as ratio- nal homogeneous spaces of Picard number 1,by a non-equidimensional analogue of the Cartan-Fubini extension principle.As an illustration we show along this line that standard embeddings between com- plex Grassmann manifolds of rank≤2 can be characterized by the VMRT-preserving property and a non-degeneracy condition,giving a new proof of a result of Neretin's which on the one hand paves the way for far-reaching generalizations to the context of rational homogeneous spaces and more generally Fano manifolds of Picard number 1,on the other hand should be applicable to the study of proper holomorphic mappings between bounded domains carrying some form of geometric structures. 相似文献
20.
C. Banica 《manuscripta mathematica》1972,6(3):207-244
We prove here a theorem, which generalizes Grauert's comparison theorem ([4], Hauptsatz IIa; cf. also Knorr [7], Vergleichssatz) and which is an analogue of a Grothéndieck's result in Algebraic Geometry ([6], Chap. III., 4.1.5). The proof makes essential use of a coherence theorem for sheaves of polynomials: Let X,Y be complex spaces, : XY a proper holomorphic map and T=(T1,...,TN) a system of indeterminates. Then, for everyO
X[T] graded sheafm, all direct image sheaves Rq*
m areY[T]-coherent. The proof is as in [2].
Diese Arbeit entstand während eines Aufenthalts des Verfassers am Fachbereich Mathematik der Universität Regensburg als Stipendiat der Alexander-von-Humboldt-Stiftung. 相似文献
Diese Arbeit entstand während eines Aufenthalts des Verfassers am Fachbereich Mathematik der Universität Regensburg als Stipendiat der Alexander-von-Humboldt-Stiftung. 相似文献