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Introduction 191 Chapter 1 Preliminaries J 93 §1 Hermitian geometry 193 §2 L estimates of d 197 Chapter 2 Isomorphism theorems for pseudo-Runge pairs 200 §1 Basic estimates 200 §2 Pseudo-Runge pairs and an approximation theorem 201 §3 Isomorphism theorems 204 §4 Examples of pseudo-Runge pairs 207 Chapter 3 Isomorphism theorems on weakly 1-complete manifolds 214 §1 Coarse isomorphism theorems 214 §2 Precise isomorphism theorems 218 Appendix 225 References 231

Isomorphism theorems for cohomology groups of weakly {1}-complete manifolds