On the reflection principle in C^n
英文摘要：
We propose a reflection principle for holomorphic objects in ${\Bbb C}^n$. Our construction generalizes the classical principle of H.Lewy, S.Pinchuk and S.Webster.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
Reflection principle and envelopes of holomorphy
The reflection function of a smooth CR diffeomorphism between two minimal real analytic hypersurfaces is everywhere real analytic.
math.CV
A reflection principle for real-analytic submanifolds of complex spaces
We give an invariant nondegeneracy condition for CR--maps between generic submanifolds in different dimensions and use it to prove a reflection principle for these maps.
math.CV
On the $C^{\infty}$ version of the reflection principle for mappings between CR manifolds
We prove a smooth version of the classical Schwarz reflection principle for CR mappings between an abstract CR manifold $M$ and a generic CR manifold embedded in euclidean complex space. As a consequence of our results, we settle a conjecture of X. Huang and provide a solution to a question raised by Forstneric.
math.CV
Riemann-Schwarz Reflection Principle and Asymptotics of Modules of Rectangular Frames
We investigate asymptotical behavior of the conformal module of a doubly-connected domain which is the difference of two homothetic rectangles under stretching it along the abscissa axis. Thereby, we give the answer to a question put by Prof. M.Vuorinen.
math.CV
An extension result of CR Functions by a general Schwarz reflection principle
It is known that a real analytic CR function f on a real analytic, generic submanifold M in C^N can be holomorphically extended. A stronger result on a finite type, real analytic, generic submanifold M is found in which we assume f a continuous CR function with real analytic imaginary part Im(f). The idea is contained in a general Schwarz Reflection Principle in one complex variable.
math.CV
On envelopes of holomorphy of domains covered by Levi-flat hats and the reflection principle
In the present paper, we associate the techniques of the Lewy-Pinchuk reflection principle with the Behnke-Sommer continuity principle. Extending a so-called reflection function to a parameterized congruence of Segre varieties, we are led to studying the envelope of holomorphy of a certain domain covered by a smooth Levi-flat ``hat''. In our main theorem, we show that every C^infty-smooth CR diffeomorphism h: M to M' between two globally minimal real analytic hypersurfaces in C^n (n >1) is real analytic at every point of M if M' is holomorphically nondegenerate. More generally, we establish th…
math.CVmath.DG
更多相关论文收起更多论文
On an analogue of Schwarz's reflection principle
We consider the Bergman space on the complex plane. We prove an analogue of Schwarz's reflection principle for unbounded quasidisks.
math.CVmath.FA
On the local geometry of generic submanifolds of C^n and the analytic reflection principle (Part I)
We build an elementary analytico-geometric theory of Segre chains and their jets.
math.CVmath.DG
Schwarz Reflection Principle, Boundary Regularity and Compactness for J-Complex Curves
We establish the Schwarz Reflection Principle for $J$-complex discs attached to a real analytic $J$-totally real submanifold of an almost complex manifold with real analytic $J$. We also prove the precise boundary regularity and derive the precise convergence in Gromov compactness theorem in $\calc^{k,α}$-classes.
math.CVmath.SG
Reflection principles for zero mean curvature surfaces in the simply isotropic 3-space
Zero mean curvature surfaces in the simply isotropic 3-space $\mathbb{I}^3$ naturally appear as intermediate geometry between geometry of minimal surfaces in $\mathbb{E}^3$ and that of maximal surfaces in $\mathbb{L}^3$. In this paper, we investigate reflection principles for zero mean curvature surfaces in $\mathbb{I}^3$ as with the above surfaces in $\mathbb{E}^3$ and $\mathbb{L}^3$. In particular, we show a reflection principle for isotropic line segments on such zero mean curvature surfaces in $\mathbb{I}^3$, along which the induced metrics become singular.
math.CVmath.DG
One sided conformal collars and the reflection principle
If a Jordan curve σ has a one-sided conformal collar with "good" properties, then, using the Reflection principle, we show that any other conformal collar of σ from the same side has the same "good" properties. A particular use of this fact concerns analytic Jordan curves, but in general the Jordan arcs we consider do not have to be analytic. We show that if an one-sided conformal collar bounded by σ is of class A^p, then any other collar bounded by σ and from the same side of σ is of class A^p.
math.CAmath.CV
Finite jet determination of CR embeddings
We prove finite jet determination results for smooth CR embeddings which are of constant degeneracy, using the method of complete systems. As an application, we derive a reflection principle for mappings between a Levi-nondegenerate hypersurface in C^N and a Levi-nondegenerate hypersurface in C^{N+1}. We also give an independent proof of the reflection principle for mappings between strictly pseudoconvex hypersurfaces in any codimension due to Forstneric.
math.CV
