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### Contents

On Factorization of Holomorphic Mappings | 1 |

Cauchy Integral Formulae and Boundary Kernel Functions | 7 |

Boundaries of Complex Manifolds | 81 |

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### Common terms and phrases

analytic set analytic space analytic subset assume automorphism Banach biholomorphic C)-group canonical cohomology compact set complex analytic family complex analytic space complex Lie group complex manifold complex space complex structure complex varieties condition connected complex contained coordinates Corollary defined deformations denote differential dimension dimensional disjoint domain element equation equivalent exists a neighborhood extended extension problem fiber bundle fibre finite formula given graded Lie algebra Hence hermitian holo holomorphic functions holomorphic mapping hypersurface imbedding induced integral intersection irreducible component isomorphism Lemma Let G Lie algebra linear Math meromorphic function metric morphic morphism non-negative divisors open neighborhood open set open subset polynomially convex projective Proof Proposition prove pseudo-convex pseudogroup resp restriction Riemann surface satisfies sheaf of germs singular Stein manifold subspace Suppose surjective tangent Theorem topological transmission problem uniform algebra unique vector bundle