### Abstract

The relationship between the Levi geometry of a submanifold of C” and the tangential Cauchy-Riemann equations is studied. On a real analytic codimension two submanifold of C”, we find conditions on the Levi algebra which allow us to locally solve the tangential Cauchy-Riemann equations (in most bidegrees) with kernels. Under the same conditions, we show that, locally, any CR-function is the boundary value jump of a holomorphic function defined on some suitable open set in C". This boundary value jump result is the best possible result because we also show that there is no one-sided extension theory for such submanifolds of C". In fact, we show that if S is a real analytic, generic, submanifold of C" (any codimension) where the excess dimension of the Levi algebra is less than the real codimension, then S is not extendible to any open set in C".

Original language | English (US) |
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Pages (from-to) | 351-374 |

Number of pages | 24 |

Journal | Transactions of the American Mathematical Society |

Volume | 272 |

Issue number | 1 |

DOIs | |

State | Published - 1982 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics