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The Hartogs phenomenon on weakly pseudoconcave hypersurfaces
Mid Sweden University, Faculty of Science, Technology and Media, Department of applied science and design.
2012 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 354, no 2, 659-683 p.Article in journal (Refereed) Published
Abstract [en]

In 2002, Henkin and Michel proved a local Hartogs phenomenon for real analytic CR functions on real analytic weakly pseudoconcave CR manifolds. The aim of the present article is to remove the assumptions on real analyticity in the case of weakly pseudoconcave hypersurfaces {Mathematical expression} . If M is a graph of class {Mathematical expression} and n ≥ 3, a global theorem is proved for the extension of holomorphic germs along M. If the appearing domains have nicely shaped boundary, a Hartogs theorem even holds for continuous CR functions, where the difference to the case of holomorphic germs relies on the possible presence of lower-dimensional CR orbits. Levi flat hypersurfaces in {Mathematical expression} require a separate treatment. Here an affirmative answer is given to the question of Tomassini, whether 2-spheres bound 3-balls in M. © 2011 Springer-Verlag.

Place, publisher, year, edition, pages
2012. Vol. 354, no 2, 659-683 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-15307DOI: 10.1007/s00208-011-0732-6ISI: 000308253400009Scopus ID: 2-s2.0-84865831031OAI: oai:DiVA.org:miun-15307DiVA: diva2:466386
Note

Correspondence Address: Porten, E.; Department of Mathematics, Mid Sweden University, Sundsvall, 85170, Sweden; email: Egmont.Porten@miun.se

Available from: 2011-12-15 Created: 2011-12-15 Last updated: 2015-07-01Bibliographically approved

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