Abstract:We solve the problems on the maximum of the conformal radius R ( D, 1) Apparently, the statement of Problem 1 has been published earlier, but we did not succeed in finding the corresponding publication. The solution of Problem 1 is obtained by using the solution of an auxiliary problem. Let 79(R0,p) be the faznily of domains in 79(R0) with given hyperbolic distance p = pD(0, 1) between the points 0 and 1.
Problem 1'. To t~nd the domain realizing the maximum Rl(p) of ~he con[ormal radius R(D, 1) in the 79( p)… Show more
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