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Another Direct Proof of Oka's Theorem (Oka IX) | Junjiro Noguchi
; | Date: |
10 Aug 2011 | Abstract: | In 1953 K. Oka IX solved in first and in a final form Levi’s problem
(Hartogs’ inverse problem) for domains or Riemann domains over $C^n$ of
arbitrary dimension. Later on a number of the proofs were given; cf. e.g.,
Docquier-Grauert’s paper in 1960, R. Narasimhan’s paper in 1961/62,
Gunning-Rossi’s book, and H"ormander’s book (in which the holomorphic
separability is pre-assumed in the definition of Riemann domains and thus the
assumption is stronger than the one in the present paper). Here we will give
another direct elementary proof of Oka’s Theorem, relying only on Grauert’s
finiteness theorem by the {it induction on the dimension} and the {it jets
over Riemann domains}; hopefully, the proof is most comprehensive. | Source: | arXiv, 1108.2078 | Services: | Forum | Review | PDF | Favorites |
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