- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:48
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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European Mathematical Society Publishing House
Zuerich, Switzerland
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123
2010
0
Holomorphic Extension from Weakly Pseudoconcave CR Manifolds
Andrea
Altomani
University of Luxembourg, LUXEMBOURG, LUXEMBOURG
C. Denson
Hill
Stony Brook University, STONY BROOK, UNITED STATES
Mauro
Nacinovich
Università di Roma Tor Vergata, ROMA, ITALY
Egmont
Porten
Mid-Sweden University, SUNDSVALL, SWEDEN
Let M be a smooth locally embeddable CR manifold, having some CR dimension m and some CR codimension d. We find an improved local geometric condition on M which guarantees, at a point p on M, that germs of CR distributions are smooth functions, and have extensions to germs of holomorphic functions on a full ambient neighborhood of p. Our condition is a form of weak pseudoconcavity, closely related to essential pseudoconcavity as introduced in [HN1]. Applications are made to CR meromorphic functions and mappings. Explicit examples are given which satisfy our new condition, but which are not pseudoconcave in the strong sense. These results demonstrate that for codimension d > 1, there are additional phenomena which are invisible when d = 1.
General
69
90
10.4171/RSMUP/123-4
http://www.ems-ph.org/doi/10.4171/RSMUP/123-4