| Introduction | p. vii |
| Harmonic, pluriharmonic, holomorphic maps and basic Hermitian and Kahlerian geometry | p. 1 |
| The general setting | p. 1 |
| The complex case | p. 6 |
| Hermitian bundles | p. 10 |
| Complex geometry via moving frames | p. 12 |
| Weitzenbock-type formulas | p. 17 |
| Comparison Results | p. 27 |
| Hessian and Laplacian comparison | p. 27 |
| Volume comparison and volume growth | p. 40 |
| A monotonicity formula for volumes | p. 58 |
| Review of spectral theory | p. 63 |
| The spectrum of a self-adjoint operator | p. 63 |
| Schrodinger operators on Riemannian manifolds | p. 69 |
| Vanishing results | p. 83 |
| Formulation of the problem | p. 83 |
| Liouville and vanishing results | p. 84 |
| Appendix: Chain rule under weak regularity | p. 99 |
| A finite-dimensionality result | p. 103 |
| Peter Li's lemma | p. 107 |
| Poincare-type inequalities | p. 110 |
| Local Sobolev inequality | p. 114 |
| L[superscript 2] Caccioppoli-type inequality | p. 117 |
| The Moser iteration procedure | p. 118 |
| A weak Harnack inequality | p. 121 |
| Proof of the abstract finiteness theorem | p. 122 |
| Applications to harmonic maps | p. 127 |
| Harmonic maps of finite L[superscript p]-energy | p. 127 |
| Harmonic maps of bounded dilations and a Schwarz-type lemma | p. 136 |
| Fundamental group and harmonic maps | p. 141 |
| A generalization of a finiteness theorem of Lemaire | p. 143 |
| Some topological applications | p. 147 |
| Ends and harmonic functions | p. 147 |
| Appendix: Further characterizations of parabolicity | p. 165 |
| Appendix: The double of a Riemannian manifold | p. 171 |
| Topology at infinity of submanifolds of C-H spaces | p. 172 |
| Line bundles over Kahler manifolds | p. 178 |
| Reduction of codimension of harmonic immersions | p. 179 |
| Constancy of holomorphic maps and the structure of complete Kahler manifolds | p. 183 |
| Three versions of a result of Li and Yau | p. 183 |
| Plurisubharmonic exhaustions | p. 199 |
| Splitting and gap theorems in the presence of a Poincare-Sobolev inequality | p. 205 |
| Splitting theorems | p. 205 |
| Gap theorems | p. 223 |
| Gap Theorems, continued | p. 229 |
| Unique continuation | p. 235 |
| L[superscript p]-cohomology of non-compact manifolds | p. 251 |
| The L[superscript p] de Rham cochain complex: reduced and unreduced cohomologies | p. 251 |
| Harmonic forms and L[superscript 2]-cohomology | p. 260 |
| Harmonic forms and L[superscript p not equal 2]-cohomology | p. 262 |
| Some topological aspects of the theory | p. 265 |
| Bibliography | p. 269 |
| Index | p. 281 |
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