JournalsrsmupVol. 123pp. 69–90

Holomorphic Extension from Weakly Pseudoconcave CR Manifolds

  • Andrea Altomani

    University of Luxembourg, Luxembourg
  • C. Denson Hill

    Stony Brook University, USA
  • Mauro Nacinovich

    Università di Roma Tor Vergata, Italy
  • Egmont Porten

    Mid-Sweden University, Sundsvall, Sweden
Holomorphic Extension from Weakly Pseudoconcave CR Manifolds cover
Download PDF

Abstract

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.

Cite this article

Andrea Altomani, C. Denson Hill, Mauro Nacinovich, Egmont Porten, Holomorphic Extension from Weakly Pseudoconcave CR Manifolds. Rend. Sem. Mat. Univ. Padova 123 (2010), pp. 69–90

DOI 10.4171/RSMUP/123-4