Extension of CR functions from boundaries in Cn x R
| Autor: | Sivaguru Ravisankar, Jiri Lebl, Alan Noell |
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| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Mathematics::Complex Variables General Mathematics 010102 general mathematics Holomorphic function Boundary (topology) Function (mathematics) Codimension 01 natural sciences Plateau's problem Omega Domain (mathematical analysis) Combinatorics Bounded function 0103 physical sciences 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Indiana University Mathematics Journal. 66:901-925 |
| ISSN: | 0022-2518 |
| DOI: | 10.1512/iumj.2017.66.6067 |
| Popis: | Let $\Omega \subset {\mathbb C}^n \times {\mathbb R}$ be a bounded domain with smooth boundary such that $\partial \Omega$ has only nondegenerate elliptic CR singularities, and let $f \colon \partial \Omega \to {\mathbb C}$ be a smooth function that is CR at CR points of $\partial \Omega$ (when $n=1$ we require separate holomorphic extensions for each real parameter). Then $f$ extends to a smooth CR function on $\bar{\Omega}$, that is, an analogue of Hartogs-Bochner holds. In addition, if $f$ and $\partial \Omega$ are real-analytic, then $f$ is the restriction of a function that is holomorphic on a neighborhood of $\bar{\Omega}$ in ${\mathbb C}^{n+1}$. An immediate application is a (possibly singular) solution of the Levi-flat Plateau problem for codimension 2 submanifolds that are CR images of $\partial \Omega$ as above. The extension also holds locally near nondegenerate, holomorphically flat, elliptic CR singularities. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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