Problem of the maximum n-th diameter

Properties of associated quadratic differentials in certain extremal problems

“…103-106]. We mention that instead of the class l~(1) in [10] one has considered the class r.'; however, the proof in [10] does not make use of the restriction b o = 0.…”

“…It has been also proved [10,Theorem 2] that no Fekete point on E can be a regular point of the differential (4).…”

“…In [10] we have established the following relation between Problem 1 and the problem of the maximum of the functional in the class y_,0), q being a fixed number (Problem 3). Here and in the sequel, by {F(f)} v we mean the coefficient of f-v in the expansion of the function F(f) in the neighborhood of the point at infinity.…”

“…coincide. Therefore, we restrict ourselves to a brief presentation of the proof of Lemma 2, referring the reader to [10] for details.…”

“…2 ~ The author's previous paper [10] is devoted to the geometric properties of the extremal configurations of Problem 1. In [10] we have established the following relation between Problem 1 and the problem of the maximum of the functional in the class y_,0), q being a fixed number (Problem 3).…”