Draft of the book on extremal length (joint with Lars Ahlfors)
Version A
Draft of the book on extremal length, version A (pdf)
Chap.I. Quelques notions et méthodes de l’analyse réelle.
- §1 Fonctions à carré intégrable, p. 1–4
- §2 Fonctions harmoniques et sous-harmoniques, p. 4bis-11
- §3 Le problème de Dirichlet, p. 12-19
Chap.II. Propriétés extrémales de représentations conformes
- §1 Représentation circulaire, p. 1–13
- §2 Longeurs et distances extrémales, p. 16–23
- §3 La correspondence des frontières, p. 24–28
Version B
Draft of the book on extremal length, version B (pdf)
- §1 End of the section with discussion of capacity, p. 56-57
- §2 Longeurs et distances extrémales, p. 58-66
- §3 La correspondence des frontières, p. 67-70
- §4 Détermination de la métrique extrémale, p. 71–76
- §5 Les lois de composition, p. 77–84
- §6 La distance extrémale dans le cas de points isolés, p. 85–102
- §7 Applications, p. 103–112
- §8 La transportation des masses, p. 113–126
Additional parts
Draft of the book on extremal length, additional parts (pdf)
- §1 Le quadrilatère, p. 1–6
- §2 Le pentagone, p. 7–20
It seems that at least two different versions of the manuscript existed. What remained of the first version consists of Chap. I and the first three sections of Chapter II.
Each section has a new numeration of the pages. The second version starts with discussion of capacity, from which only two pages (56–57) survived and then covers sections 2–8 of Chap. II.
The additional parts look close to the Ahlfors talk at the 10th Scandinavian Math. Congress at Copenhagen, 1946. Some figures in this part are hardly visible.
According to this description, we rearranged the material into three files.
The location of the original manuscripts remains unknown to us. We have not seen them, and we worked only with their copies in pdf format.