Contents Introduction vii Acknowledgements xiii Chapter 1. The Local Theory of the Cauchy Problem 1 Chapter 2. The “Road Map”: The Concentration Compactness/Rigidity Theorem Method for Critical Problems I 17 Chapter 3. The “Road Map”: The Concentration Compactness/Rigidity Theorem Method for Critical Problems II 31 Chapter 4. Properties of Compact Solutions and Some More Rigidity Theorems, with Applications to an Extension of Theorem 2.6 45 Chapter 5. Proof of the Rigidity Theorems 69 Chapter 6. Type II Blow-up Solutions 81 Chapter 7. Channels of Energy and Outer Energy Lower Bounds 101 Chapter 8. Universal Type II Blow-up Profiles 109 Chapter 9. Soliton Resolution for Radial Solutions to (NLW), I 121 Chapter 10. Soliton Resolution for Radial Solutions to (NLW), II 135 Chapter 11. Soliton Resolution for Radial Solutions to (NLW), III 145 Bibliography 157 v
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