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1.
In this paper we solve the problem of local pseudohermitian embeddability into spheres. We state necessary and sufficient
conditions for the embeddability as a finite number of equations and rank conditions on the curvature and torsion tensors
and their derivatives.
The second author was supported by BK21-Yonsei University 相似文献
2.
Jiří Lebl 《Journal of Geometric Analysis》2007,17(2):321-341
A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension
is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being
contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely
resolved for algebraic submanifolds of codimension 2 and a sufficient condition for noncontainment is given for non algebraic
submanifolds. As a consequence, an example of a submanifold of codimension 2, not biholomorphically equivalent to an algebraic
one, is given. We also investigate the structure of singularities of Levi-flat hypersurfaces. 相似文献
3.
Peter Ebenfelt 《Mathematische Annalen》2002,322(3):583-602
Let be a connected real-analytic hypersurface containing a connected complex hypersurface , and let be a smooth CR mapping sending M into another real-analytic hypersurface . In this paper, we prove that if f does not collapse E to a point and does not collapse M into the image of E, and if the Levi form of M vanishes to first order along E, then f is real-analytic in a neighborhood of E. In general, the corresponding statement is false if the Levi form of M vanishes to second order or higher, in view of an example due to the author. We also show analogous results in higher dimensions
provided that the target M' satisfies a certain nondegeneracy condition. The main ingredient in the proof, which seems to be of independent interest,
is the prolongation of the system defining a CR mapping sending M into M' to a Pfaffian system on M with singularities along E. The nature of the singularity is described by the order of vanishing of the Levi form along E.
Received: 12 February 2001 / Published online: 18 January 2002 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.
In this paper we solve local CR embeddability problem of smooth CR manifolds into spheres under a certain nondegeneracy condition
on the Chern–Moser’s curvature tensor. We state necessary and sufficient conditions for the existence of CR embeddings as
finite number of equations and rank conditions on the Chern–Moser’s curvature tensors and their derivatives. We also discuss
the rigidity of those embeddings.
J.-W. Oh was partially supported by BK21-Yonsei University. 相似文献
6.
7.
Robert Juhlin 《Advances in Mathematics》2009,222(5):1611-1648
We prove that if M is a connected real-analytic holomorphically nondegenerate hypersurface in Cn+1, then for any point p∈M there exists an integer k such that any two germs at p of local biholomorphic mappings that send M into itself and whose k-jets agree at p are identical.The above is a special case of a more general theorem stated for formal hypersurfaces that gives a finite jet determination result for the class of formal mappings whose Jacobian determinant does not vanish identically. 相似文献
8.
In this paper we consider a classical regularity problem for biholomorphisms between two bounded real-analytic domains. It
is proved that such biholomorphisms can be holomorphically extended through the boundaries of the domains in a space of complex
dimension 2.
Communicated by Steven Krantz 相似文献
9.
Baouendi M. S. Mir Nordine Rothschild Linda Preiss 《Journal of Geometric Analysis》2002,12(4):543-580
Results on finite determination and convergence of formal mappings between smooth generic submanifolds in ℂ
N
are established in this article. The finite determination result gibes sufficient conditions to guarantee that a formal map
is uniquely determined by its jet, of a preassigned order, at a point. Convergence of formal mappings for real-analytic generic
submanifolds under appropriate assumptions is proved, and natural geometric conditions are given to assure that if two germs
of such submanifolds are formally equivalent, then, they are necessarily biholomorphically equivalent. It is also shown that
if two real-algebraic hypersurfaces in ℂ
N
are biholomorphically equivalent, then, they are algebraically equivalent. All the results are first proved in the more general
context of “reflection ideals” associated to formal mappings between formal as well as real-analytic and real-algebraic manifolds. 相似文献
10.
V. V. Ežov 《Journal of Geometric Analysis》1992,2(5):417-427
LetM ? ?n be a real-analytic, nonspherical hypersurface passing through the origin and having nondegenerate Levi form. Let Aut0 M be the stability group of 0. Whenn = 12 an example is constructed for which Aut0 M cannot be linearized. 相似文献
11.
We consider holomorphic mappings sending a given Levi-nondegenerate pseudoconcave hypersurface M in Cn+1 into a nondegenerate hyperquadric of the same signature in PCN+1 and show that if M is sufficiently close to a hyperquadric in a certain sense, then any two such mappings differ only by an automorphism of the hyperquadric. 相似文献
12.
B. M. Braga 《Journal of Functional Analysis》2018,274(11):3149-3169
In this paper, we study nonlinear embeddings between Banach spaces. More specifically, the goal of this paper is to study weaker versions of coarse and uniform embeddability, and to provide suggestive evidences that those weaker embeddings may be stronger than one would think. We do such by proving that many known results regarding coarse and uniform embeddability remain valid for those weaker notions of embeddability. 相似文献
13.
Judith Brinkschulte 《manuscripta mathematica》2006,120(2):181-192
We show that the Hartogs phenomenon holds in minimal, weakly 2-pseudoconcave generic C R submanifolds of a Stein manifold with trivial normal bundle. We also prove some results concerning the local and/or global solvability of the tangential Cauchy-Riemann equations for smooth forms and currents on weakly q-pseudoconcave C R manifolds. 相似文献
14.
15.
The strong embeddability is a notion of metric geometry, which is an intermediate property lying between coarse embeddability and property A. In this paper, we study the permanence properties of strong embeddability for metric spaces. We show that strong embeddability is coarsely invariant and it is closed under taking subspaces, direct products, direct limits and finite unions. Furthermore, we show that a metric space is strongly embeddable if and only if it has weak finite decomposition complexity with respect to strong embeddability. 相似文献
16.
We study degree spectra of structures with respect to the bi‐embeddability relation. The bi‐embeddability spectrum of a structure is the family of Turing degrees of its bi‐embeddable copies. To facilitate our study we introduce the notions of bi‐embeddable triviality and basis of a spectrum. Using bi‐embeddable triviality we show that several known families of degrees are bi‐embeddability spectra of structures. We then characterize the bi‐embeddability spectra of linear orderings and study bases of bi‐embeddability spectra of strongly locally finite graphs. 相似文献
17.
18.
It was once conjectured that if A is a uniform algebra on its maximal ideal space X, and if each point of X is a peak point for A, then A = C(X). This peak point conjecture was disproved by Brian Cole in 1968. However, Anderson and Izzo showed that the peak point conjecture
does hold for uniform algebras generated by smooth functions on smooth two-manifolds with boundary. The corresponding assertion
for smooth three-manifolds is false, but Anderson, Izzo, and Wermer established a peak point theorem for polynomial approximation
on real-analytic three-manifolds with boundary. Here we establish a more general peak point theorem for real-analytic three-manifolds
with boundary analogous to the two-dimensional result. We also show that if A is a counterexample to the peak point conjecture generated by smooth functions on a manifold of arbitrary dimension, then
the essential set for A has empty interior. 相似文献
19.
《复变函数与椭圆型方程》2012,57(10):939-951
Let Ω be a bounded, weakly pseudoconvex domain in C n , n ≤ 2, with real-analytic boundary. A real-analytic submanifold M ? ?Ω is called an analytic interpolation manifold if every real-analytic function on M extends to a function belonging to (Ω¯). We provide sufficient conditions for M to be an analytic interpolation manifold. We give examples showing that neither of these conditions can be relaxed, as well as examples of analytic interpolation manifolds lying entirely within the set of weakly pseudoconvex points of ?Ω. 相似文献
20.
本文定义了George和Veeramani意义下的模糊度量空间的强嵌入,证明了可强嵌入的模糊度量空间能够粗嵌入到Hilbert空间.另外还证明了强嵌入在模糊度量空间的粗范畴下是不变的,并给出了模糊度量空间强嵌入的一些等价刻画. 相似文献