Two-dimensional slices of nonpseudoconvex domains with rough boundary

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• 作者：Egmont Porten (1)
  
• 关键词：Pseudoconvexity ; Sections of nonpseudoconvex domains ; Continuity principle ; 32T05 ; 32D20 ; 32D26 ; 32A40
• 刊名：Mathematische Zeitschrift
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：278
• 期：1-2
• 页码：19-23
• 全文大小：132 KB
• 参考文献：1. Grauert, H., Remmert, R.: Konvexit盲t in der komplexen analysis. Comment. Math. Helvetici 31, 152鈥?83 (1956) CrossRef
  2. Hitotumatu, S.: On some conjectures concerning pseudo-convex domains. J. Math. Soc. Jpn. 6, 177鈥?95 (1954) CrossRef
  3. H枚rmander, L.: An Introduction to Complex Analysis in Several Variables. North-Holland, Amsterdam (1990)
  4. Jarnicki, M., Pflug, P.: Extension of holomorphic functions. De Gruyter Expositions in Mathematics, vol. 34. Walter de Gruyter, Berlin (2000) CrossRef
  5. Jacobson, R.: Pseudoconvexity is a two-dimensional phenomenon. Preprint arXiv:0907.1304v1
  6. Nikolov, N., Pflug, P.: Two-dimensional slices on non-pseudoconvex open sets. Math. Z. 272, 381鈥?88 (2012) CrossRef
  7. Nikolov, N., Thomas, P.J.: Rigid characterizations of pseudoconvex domains. Indiana Univ. Math. J. 61, 1313鈥?323 (2012) CrossRef
  8. Porten, E.: On the Hartogs-phenomenon and extension of analytic hypersurfaces in non-separated Riemann domains. Complex Var. 47, 325鈥?32 (2002) CrossRef
  
• 作者单位：Egmont Porten (1)
  
  1. Department for Science Education and Mathematics, Mid Sweden University, Sundsvall聽, 85170, Sweden
  
• ISSN：1432-1823

文摘

For a domain \(D\subset {\mathbb C}^n,\; n\ge 3\) , the set \(E\) is defined as the set of all points \(z\in {\mathbb C}^n\) for which the intersection of \(D\) with every complex \(2\) -plane through \(z\) is pseudoconvex. For \(D\) nonpseudoconvex, it is shown that \(E\) is contained in an affine subspace of codimension \(2\) . This results solves a problem raised by Nikolov and Pflug.