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目次

Preface vii Chapter 1. Background Material 1 1.1 Riemannian Geometry 11.2 Basics in Nonlinear Analysis 7 Chapter 2. The Model Equations 13 2.1Palais-Smale Sequences 14 2.2 Strong Solutions of Minimal Energy 17 2.3Strong Solutions of High Energies 19 2.4 The Case of the Sphere 23 Chapter3. Blow-up Theory in Sobolev Spaces 25 3.1 The H 2/1-Decomposition forPalais-Smale Sequences 26 3.2 Subtracting a Bubble and Nonnegative Solutions32 3.3 The De Giorgi-Nash-Moser Iterative Scheme for Strong Solutions 45Chapter 4. Exhaustion and Weak Pointwise Estimates 51 4.1 Weak PointwiseEstimates 52 4.2 Exhaustion of Blow-up Points 54 Chapter 5. AsymptoticsWhen the Energy Is of Minimal Type 67 5.1 Strong Convergence and Blow-up 685.2 Sharp Pointwise Estimates 72 Chapter 6. Asymptotics When the Energy IsArbitrary 83 6.1 A Fundamental Estimate: 1 88 6.2 A Fundamental Estimate: 2143 6.3 Asymptotic Behavior 182 Appendix A. The Green's Function on CompactManifolds 201 Appendix B. Coercivity Is a Necessary Condition 209Bibliography 213