## Andreotti-Grauert Theory by Integral Formulas |

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### Contents

INTEGRAL FORMULAS AND FIRST APPLICATIONS | 9 |

The MartinelliBochnerKoppelman formula and the Kodaira finite | 21 |

CauchyFantappie formulas the Poincare slemma the Dolbeault | 34 |

Copyright | |

20 other sections not shown

### Common terms and phrases

a q—concave Appendix assertions hold true assume Banach space bidegree 0,r bounded linear operator C1 boundary C2 function canonical Leray map Cauchy—Fantappie formula closed with respect compact complex manifold compact set compact subsets compact support continuous differential form continuous linear convex Corollary defined definition degenerate critical points denote Dolbeault cohomology E—valued current exhausting function exist a neighborhood extension element follows from Theorem form f Fréchet space Hence holomorphic coordinates holomorphic functions holomorphic vector bundle implies integral isomorphism Lemma Let D cc moreover n—dimensional complex manifold non—degenerate strictly q—concave non—degenerate strictly q—convex obtain Ogqgn—l open sets Proof of Proposition proof of Theorem pseudoconvex q—concave extension q+1)—convex function relatively compact Remark resp restriction map Sect sequence singular strictly increasing strictly plurisubharmonic strictly q—concave domain strictly q—convex domain subspace sufficient to prove sufficiently small supp surjective topology ueD_ uniform convergence uniform estimates