Hans Ringstrom, KTH Royal Institute of Technology, Stockholm, Sweden
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Description
1. Introduction 2. Basic notions and previous results 3. Assumptions 4. Results and outline 2. Geometry 5. Basic properties of the frame adapted to the eigenspaces of $\mathcal {K}$ 6. Lie derivatives of the frame 7. Estimating the norm of the elements of the frame 8. Function spaces and estimates 9. Higher order estimates of the Lie derivatives of the elements of the frame 10. Estimates of the components of the metric 3. Wave Equations 11. Systems of wave equations, basic energy estimate 12. Commutators 13. Higher order energy estimates, part I 14. Higher order energy estimates, part II 15. Localising the analysis 16. Energy estimates in causally localised regions 17. Deriving asymptotics 18. Specifying the asymptotics 4. Appendices A. Terminology and justification of assumptions B. Gagliardo-Nirenberg estimates C. Examples