ON SMOOTH AND ANALYTIC DISKS IN C-2 WITH COMMON BOUNDARY
SCIE
- Title
- ON SMOOTH AND ANALYTIC DISKS IN C-2 WITH COMMON BOUNDARY
- Authors
- KIM, KT
- Date Issued
- 1994-10
- Publisher
- AMER MATHEMATICAL SOC
- Abstract
- We construct explicitly a real analytic embedded real two-dimensional disk in C-2 totally real except at exactly one elliptic complex tangent point, which shares the common boundary with an analytic disk in the same C-2, but does not contain this analytic disk in its envelope of holomorphy. The same proof further yields an explicit example of a holomorphic re-embedding of the standard two-sphere into C-2 in such a way that the new embedding shows some exceptional properties: It bounds a real three-dimensional Levi flat cell in C-2 foliated by analytic disks, which is not polynomially convex. In particular, this new embedding of the standard two-sphere cannot be a subset of any compact strongly pseudoconvex surface in C-2 or a subset of any strongly pseudoconvex graph in C-2 in the sense of Bedford and Gaveau.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/27949
- DOI
- 10.2307/2161046
- ISSN
- 0002-9939
- Article Type
- Article
- Citation
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 122, no. 2, page. 541 - 544, 1994-10
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