共查询到20条相似文献,搜索用时 15 毫秒
1.
Jasmin Raissy 《Mathematische Zeitschrift》2010,264(4):881-900
Let f be a germ of holomorphic diffeomorphism of
\mathbb Cn{\mathbb {C}^{n}} fixing the origin O, with d f
O
diagonalizable. We prove that, under certain arithmetic conditions on the eigenvalues of d f
O
and some restrictions on the resonances, f is locally holomorphically linearizable if and only if there exists a particular f -invariant complex manifold. Most of the classical linearization results can be obtained as corollaries of our result. 相似文献
2.
Let D be a convex domain with smooth boundary in complex space and let f be a continuous function on the boundary of D. Suppose that f holomorphically extends to the extremal discs tangent to a convex subdomain of D. We prove that f holomorphically extends to D. The result partially answers a conjecture by Globevnik and Stout of 1991. 相似文献
3.
Let Δ be the open unit disc in, let pbΔ, and let f be a continuous function on which extends holomorphically from each circle in centered at the origin and from each circle in which passes through p. Then f is holomorphic on Δ. 相似文献
4.
Mark L. Agranovsky 《Advances in Mathematics》2007,211(1):284-326
We prove that homologically nontrivial generic smooth (2n−1)-parameter families of analytic discs in Cn, n?2, attached by their boundaries to a CR-manifold Ω, test CR-functions in the following sense: if a smooth function on Ω analytically extends into any analytic discs from the family, then the function satisfies tangential CR-equations on Ω. In particular, we give an answer (Theorem 1) to the following long standing open question, so called strip-problem, earlier solved only for special families (mainly for circles): given a smooth one-parameter family of Jordan curves in the plane and a function f admitting holomorphic extension inside each curve, must f be holomorphic on the union of the curves? We prove, for real-analytic functions and arbitrary generic real-analytic families of curves, that the answer is “yes,” if no point is surrounded by all curves from the family. The latter condition is essential. We generalize this result to characterization of complex curves in C2 as real 2-manifolds admitting nontrivial families of attached analytic discs (Theorem 4). The main result implies fairly general Morera type characterization of CR-functions on hypersurfaces in C2 in terms of holomorphic extensions into three-parameter families of attached analytic discs (Theorem 2). One of the applications is confirming, in real-analytic category, the Globevnik-Stout conjecture (Theorem 3) on boundary values of holomorphic functions. It is proved that a smooth function on the boundary of a smooth strictly convex domain in Cn extends holomorphically inside the domain if it extends holomorphically into complex lines tangent to a given strictly convex subdomain. The proofs are based on a universal approach, namely, on the reduction to a problem of propagation, from the boundary to the interior, of degeneracy of CR-foliations of solid torus type manifolds (Theorem 2.2). 相似文献
5.
Let D be a bounded domain in C
n (n>1) with a connected smooth boundary D and let f be a continuous function on D. We consider conditions (generalizing those of the Hartogs–Bochner theorem) for holomorphic extendability of f to D. As a corollary we derive some boundary analog of Morera's theorem claiming that if the integrals of f vanish over the intersection of the boundary of the domain with complex curves in some class then f extends holomorphically to the domain. 相似文献
6.
For a domain D ? ? n we construct a continuous foliation of D into one-real-dimensional curves such that any function f ∈ C 1(D) which can be extended holomorphically into some neighborhood of each curve in the foliation will be holomorphic on D. 相似文献
7.
Dejan Kolari? 《Differential Geometry and its Applications》2011,29(3):292-298
We prove the parametric homotopy principle for holomorphic immersions of Stein manifolds into Euclidean space and the homotopy principle with approximation on holomorphically convex sets. We write an integration by parts like formula for the solution f to the problem LfΣ|=g, where L is a holomorphic vector field, semi-transversal to analytic variety Σ. 相似文献
8.
Josip Globevnik 《Arkiv f?r Matematik》2005,43(2):383-393
It is well known that every Hölder continuous function on the unit circle is the sum of two functions such that one of these functions extends holomorphically into the unit disc and the other extends holomorphically into the complement of the unit disc. We prove that an analogue of this holds for Hölder continuous functions on an annulus A which have zero averages on all circles contained in A which surround the hole. 相似文献
9.
Pavel Pyrih 《Potential Analysis》1992,1(4):373-378
We consider fine topology in the complex plane C and finely harmonic morphisms. We use oriented Jordan curves in the plane to prove that for a finely locally injective finely harmonic morphism f in a fine domain in C, either f or f is a finely holomorphic function. This partially extends result by Fuglede, who considered a kind of continuity for the fine derivatives of the finely harmonic morphism. As a consequence of this we obtain a both necessary and sufficient condition for a function f to be finely holomorphic or finely antiholomorphic. We do not know if the condition of finely local injectivity (q.e.) is automatically fulfilled by any non-constant finely harmonic morphism. 相似文献
10.
We describe domains to which the Hua Loo-Keng-type integral for the Lie ball extends holomorphically. We obtain a criterion for the possibility of holomorphic extension of functions from part of the Lie sphere to the Lie ball. 相似文献
11.
Rasul Shafikov 《Mathematische Zeitschrift》2002,242(3):517-528
We show that a proper holomorphic mapping from a domain with real-analytic boundary to a domain with real-algebraic boundary extends holomorphically to a neighborhood of .
Received: 14 March 2001 / Published online: 1 February 2002 相似文献
12.
Filippo Bracci Roberto Tauraso Fabio Vlacci 《Journal of Mathematical Analysis and Applications》2002,270(2):1131-473
Let f,g be two commuting holomorphic self-maps of the unit disc. If f and g agree at the common Wolff point up to a certain order of derivatives (no more than 3 if the Wolff point is on the unit circle), then f≡g. 相似文献
13.
Alekos Vidras 《Mathematische Nachrichten》1997,187(1):267-292
It is proven in the present article that the solutions of infinite order differential equation with holomorphic parameter w ∈ U ? ? depend holomorphically on w in the neighborhood of characteristic points of certain directions. 相似文献
14.
Jasmin Raissy 《Journal of Geometric Analysis》2010,20(2):472-524
Let f be a germ of biholomorphism of ℂ
n
, fixing the origin. We show that if the germ commutes with a torus action, then we get information on the germs that can
be conjugated to f, and furthermore on the existence of a holomorphic linearization or of a holomorphic normalization of f. We find out in a complete and computable manner what kind of structure a torus action must have in order to get a Poincaré-Dulac
holomorphic normalization, studying the possible torsion phenomena. In particular, we link the eigenvalues of df
O
to the weight matrix of the action. The link and the structure we found are more complicated than what one would expect;
a detailed study was needed to completely understand the relations between torus actions, holomorphic Poincaré-Dulac normalizations,
and torsion phenomena. We end the article giving an example of techniques that can be used to construct torus actions. 相似文献
15.
We consider a real analytic foliation of by complex analytic manifolds of dimension m issued transversally from a CR generic submanifold of codimension m. We prove that a continuous CR function f on M which has separate holomorphic extension along each leaf, is holomorphic. When the leaves are cartesian straight planes,
separate holomorphic extension along suitable selections of these planes suffices and f turns out to be holomorphic in a neighbourhood of their union. If M is a hypersurface we can also specify the side of the extension, regardless the leaves are straight or not. 相似文献
16.
Mikhail Verbitsky 《Geometric And Functional Analysis》1996,6(4):601-611
We announce the structure theorem for theH
2(M)-generated part of cohomology of a compact hyperkähler manifold. This computation uses an action of the Lie algebra so(4,n–2) wheren=dimH
2(M) on the total cohomology space ofM. We also prove that every two points of the connected component of the moduli space of holomorphically symplectic manifolds can be connected with so-called twistor lines — projective lines holomorphically embedded in the moduli space and corresponding to the hyperkähler structures. This has interesting implications for the geometry of compact hyperkähler manifolds and of holomorphic vector bundles over such manifolds. 相似文献
17.
Let ƒ: D → D′ be a proper holomorphic mapping between bounded domains D, D′ in ℂ2.Let M, M′ be open pieces on δD, δD′, respectively that are smooth, real analytic and of finite type. Suppose that the cluster
set of M under ƒ is contained in M′. It is shown that ƒ extends holomorphically across M. This can be viewed as a local version
of the Diederich-Pinchuk extension result for proper mappings in ℂ2. 相似文献
18.
Let f be a generalized holomorphic function on a connected open set
W ì \Bbb C\Omega\subset {\Bbb C}
. It is proved that f equals zero if and only if there exists a smooth curve and a set A of positive (one-dimensional) measure such that f takes zero value on A. Also, a holomorphic generalized function different from zero on the disc, which takes zero values on a dense G
δ-set of the disc, is constructed. The generalized zero set of a holomorphic function is introduced and studied in an analogous
way. 相似文献
19.
Charles J. K. Batty Mark D. Blake Sachi Srivastava 《Integral Equations and Operator Theory》2003,45(2):125-154
Let
f : \mathbbR+ ? \mathbbC f : \mathbb{R}_{+} \longrightarrow \mathbb{C} be an exponentially bounded, measurable function. We introduce a growth bound z(f) \zeta(f) which measures the extent to which f f can be approximated by holomorphic functions. This growth bound is related to the location of the domain of holomorphy of the Laplace transform of f f far from the real axis. The denition extends to vector and operator-valued cases. For a C0 C_{0} -semigroup T T of operators, z(T) \zeta(T) is closely related to the critical growth bound of T T . 相似文献
20.
Nordine Mir 《Mathematische Zeitschrift》1999,231(1):189-202
We give a new algebraic characterization of holomorphic nondegeneracy for embedded real algebraic hypersurfaces in , . We then use this criterion to prove the following result about real analyticity of smooth CR mappings: any smooth CR mapping
H between a real analytic hypersurface and a rigid polynomial holomorphically nondegenerate hypersurface is real analytic,
provided the map H is not totally degenerate in the sense of Baouendi and Rothschild.
Received September 19, 1997 相似文献