tailieunhanh - Đề tài " A proof of the Kepler conjecture "

This project would not have been possible without the generous support of many people. I would particularly like to thank Kerri Smith, Sam Ferguson, Sean McLaughlin, Jeff Lagarias, Gabor Fejes T´oth, Robert MacPherson, and the referees for their support of this project. A more comprehensive list of those who contributed to this project in various ways appears in [Hal06b]. | Annals of Mathematics A proof of the Kepler conjecture By Thomas C. Hales Annals of Mathematics 162 2005 1065 1185 A proof of the Kepler conjecture By Thomas C. Hales To the memory of László Fejes Toth Contents Preface 1. The top-level structure of the proof . Statement of theorems . Basic concepts in the proof . Logical skeleton of the proof . Proofs of the central claims 2. Construction of the Q-system . Description of the Q-system . Geometric considerations . Incidence relations . Overlap of simplices 3. V -cells . V -cells . Orientation . Interaction of V-cells with the Q-system 4. Decomposition stars . Indexing sets . Cells attached to decomposition stars . Colored spaces 5. Scoring Ferguson Hales . Definitions . Negligibility . Fcc-compatibility . Scores of standard clusters 6. Local optimality . Results . Rogers simplices . Bounds on simplices . Breaking clusters into pieces . Proofs This research was supported by a grant from the NSF over the period 1995-1998. 1066 THOMAS C. HALES 7. Tame graphs . Basic definitions . Weight assignments . Plane graph properties 8. Classification of tame plane graphs . Statement of the theorems . Basic definitions . A finite state machine . Pruning strategies 9. Contravening graphs . A review of earlier results . Contravening plane graphs defined 10. Contravention is tame . First properties . Computer calculations and their consequences . Linear programs . A non-contravening 4-circuit . Possible 4-circuits 11. Weight assignments . Admissibility . Proof that tri v 2 . Bounds when tri v e 3 4 . Weight assignments for aggregates 12. Linear program estimates . Relaxation . The linear programs . Basic linear programs . Error analysis 13. Elimination of aggregates . Triangle and quad branching . A pentagonal hull with n 8 . n 8 hexagonal hull . n 7 pentagonal hull .