# On an $n$-manifold in $\mathbf{C}^n$ near an elliptic complex tangent

@article{Huang1998OnA,
title={On an \$n\$-manifold in \$\mathbf\{C\}^n\$ near an elliptic complex tangent},
author={Xiaojun Huang},
journal={Journal of the American Mathematical Society},
year={1998},
volume={11},
pages={669-692}
}
• Xiaojun Huang
• Published 1 July 1998
• Mathematics
• Journal of the American Mathematical Society
In this paper, we will be concerned with the local biholomorphic properties of a real n-manifold M in C. At a generic point, such a manifold basically has the nature of the standard R in C. Near a complex tangent, however, the consideration can be much more complicated and the manifold may acquire a nontrivial local hull of holomorphy and many other biholomorphic invariants. The study of such a problem was first carried out in a celebrated paper of E. Bishop [BIS] where, for each sufficiently…
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## References

SHOWING 1-10 OF 25 REFERENCES
Normal forms for real surfaces in C2 near complex tangents and hyperbolic surface transformations
• Mathematics
• 1983
It is well known that the complex analytical properties of a real submanifold M in the complex space C n are most accessible through consideration of the complex tangents to M. The properties we have
On a problem of Moser
• Mathematics
• 1995
1 0 Introduction This paper studies the analytic structure of the local hull of holomorphy of a 2-dimensional, real analytic manifold that is embedded in C 2. Our specific purpose is to solve a
Geometric analysis in several complex variables
• Mathematics
• 1994
In this thesis, we answer several questions in the function theory of several complex variables which possess local geometric features but which need global non-linear analysis method for the
Complex tangents of real surfaces in complex surfaces
Introduction. In this paper we study the complex tangents of real surfaces in complex surfaces. More precisely, let M be a closed real surface, i.e., a smooth, compact, two-dimensional manifold
Analytic surfaces in C^2 and their local hull of holomorphy
a) We consider real analylic surfaces M (i.e. dim*M:2) in C2. Two such surfaces M, ft are called equivalent if they can be mapped into each olher by a mapping which is biholomorphic in the complex
Geometry of Low-dimensional Manifolds: Filling by holomorphic discs and its applications
The survey is devoted to application of the technique of filling by holomorphic discs to different symplectic and complex analytic problems. COMPLEX AND SYMPLECTIC RECOLLECTIONS J -Convexity Let X, J
Pseudo holomorphic curves in symplectic manifolds
Definitions. A parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J). The image C=f(S)C V is called
CR Manifolds and the Tangential Cauchy-Riemann Complex
PRELIMINARIES. Differential Forms and Stokes Theorem. Distributions and Curents. Fundamental Solutions for(these symbols are to be used in an equation -----? ? z ---- see note at bottom)and D. Edge
EXTENSION OF CR FUNCTIONS INTO A WEDGE FROM A MANIFOLD OF FINITE TYPE
It is shown that, if a generating manifold does not contain proper submanifolds of the same CR dimension as , then all CR functions can be extended from into some wedge with edge . In particular,
Nonlinear functional analysis
This graduate-level text offers a survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis. It features extensive commentary, many examples, and interesting,