Teichmüller's Theorem in Higher Dimensions and Its Applications
Matti Vuorinen; Toshiyuki Sugawa; Anatoly Golberg
Teichmüller's Theorem in Higher Dimensions and Its Applications
Matti Vuorinen
Toshiyuki Sugawa
Anatoly Golberg
SPRINGER HEIDELBERG
Julkaisun pysyvä osoite on:
https://urn.fi/URN:NBN:fi-fe2022012711082
https://urn.fi/URN:NBN:fi-fe2022012711082
Tiivistelmä
For a given ring (domain) in (R) over bar (n), we discuss whether its boundary components can be separated by an annular ring with modulus nearly equal to that of the given ring. In particular, we show that, for all n >= 3, the standard definition of uniformly perfect sets in terms of the Euclidean metric is equivalent to the boundedness of the moduli of the separating rings. We also establish separation theorems for a "half" of a ring. As applications of those results, we will prove boundary Holder continuity of quasiconformal mappings of the ball or the half space in R-n.
Kokoelmat
- Rinnakkaistallenteet [19207]