Uniformly perfect sets: their analytical and geometrical aspects. (English. Japanese original) Zbl 1247.30040
Sugaku Expo. 16, No. 2, 225-242 (2003); translation from Sūgaku 53, No. 4, 387-402 (2001).
From the introduction: “In this survey, we give an exposition of the notion of uniform perfectness, which is a quantified version of perfectness; and, in spite of the apparent simplicity of its definition, we will see that uniform perfectness yields important information on the metric structure of a set even in the case when it is totally disconnected. This property is indeed enjoyed by most compact sets that have a certain self-similarity.”
For more details see the author’s survey in [Complex Variables, Theory Appl. 36, No. 4, 311–345 (1998; Zbl 0915.30039)].
For more details see the author’s survey in [Complex Variables, Theory Appl. 36, No. 4, 311–345 (1998; Zbl 0915.30039)].
MSC:
| 30C85 | Capacity and harmonic measure in the complex plane |
| 30F35 | Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) |
| 30F40 | Kleinian groups (aspects of compact Riemann surfaces and uniformization) |
| 30F60 | Teichmüller theory for Riemann surfaces |
| 37F30 | Quasiconformal methods and Teichmüller theory, etc. (dynamical systems) (MSC2010) |
