Sharp distortion theorems for quasiconformal mappings

G. D. Anderson, M. K. Vamanamurthy, M. Vuorinen
1988 Transactions of the American Mathematical Society  
Continuing their earlier work on distortion theory, the authors prove some dimension-free distortion theorems for if-quasiconformal mappings in R". For example, one of the present results is the following sharp variant of the Schwarz lemma: If / is a /T-quasiconformal self-mapping of the unit ball B", n > 2, with /(0) = 0, üien4l-K2\x\K ^\f(x)\ 1, and RTn{t), t > 0, respectively. Their (conformai) capacities are denoted as in [AW] by y(s) = y"(s) = c&pRGn(s), s>l, r(t) = r"{t) -capÄr,n(0, t >
more » ... ) -capÄr,n(0, t > 0. These functions satisfy the basic functional identity (1.1) y(s) = 2"-lT(s2 -1), s>l. We sometimes omit the subscript « if there is no danger of confusion.
doi:10.1090/s0002-9947-1988-0920148-1 fatcat:42pmexobzbee5ft3iahkywwn5q