Flattening of CR singular points and analyticity of the local hull of holomorphy I
نویسندگان
چکیده
This is the first article of the two papers in which we investigate the holomorphic and formal flattening problem for a codimension two real submanifold in C with n ≥ 3 near a non-degenerate CR singular point. The problem is motivated from the study of the complex Plateau problem that seeks for the Levi-flat hypersurface bounded by a given real submanifold and is motivated by the classical complex analysis problem of finding the local hull of holomorphy of a real submanifold in a complex space. The present article is focused on the case of CR singular points with at least one elliptic direction. We solve the holomorphic flattening problem and thus provide a complete description of the local hull of holomorphy in this setting. The results in this paper and those in [HY3] are taken from our arxiv post [HY4]. We split [HY4] into two independent articles to avoid it being too long.
منابع مشابه
Flattening of CR singular points and analyticity of the local hull of holomorphy II
This is the second article of the two papers, in which we investigate the holomorphic and formal flattening problem of a non-degenerate CR singular point of a codimension two real submanifold in C with n ≥ 3. The problem is motivated from the study of the complex Plateau problem that looks for the Levi-flat hypersurface bounded by a given real submanifold and by the classical complex analysis p...
متن کاملAn Improved N-dimensional NURBs-based Metamodel
Non Uniform Rational B-splines (NURBs) are proved to be very promising for metamodeling in engineering problems, because they have unique properties such as local modification scheme, strong convex hull property, and infinitely differentiability, etc. Since NURBs are defined by control points, knot vector, and weights associated with control points, the precision of NURBs is influenced by all o...
متن کاملSweep Line Algorithm for Convex Hull Revisited
Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...
متن کاملDetecting the location of the boundary layers in singular perturbation problems with general linear non-local boundary conditions
Singular perturbation problems have been studied by many mathematicians. Since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. This paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...
متن کامل