TY - JOUR
T1 - Harmonic measure of continua with a fixed diameter
AU - Solynin, A. Yu
PY - 1987/8
Y1 - 1987/8
N2 - Let e{open} be the family of all continua E in {Mathematical expression}, where U={|z| < 1}, let U(E) be the connected component of UE containing the point z=0, let wE(z0=w(z0, E, U(E)) be the harmonic measure of E relative to the domain U(E) at the point z0 ∃ U(E). In the paper one answers affirmatively a question raised by B. Rodkin [K. F. Barth, D. A. Branna, and W. K. Hayman, "Research problems in complx analysis," Bull. London Math. Soc., l6, No. 5, 490-517, 1984]. Namely, one proves that in the family e{open}(d0) of continua E ∃ e{open}, satisfying the condition diam E=d0,o0≤2, one has the inequality {Mathematical expression} arcsin d0/2, one indicates all the cases for which equality prevails.
AB - Let e{open} be the family of all continua E in {Mathematical expression}, where U={|z| < 1}, let U(E) be the connected component of UE containing the point z=0, let wE(z0=w(z0, E, U(E)) be the harmonic measure of E relative to the domain U(E) at the point z0 ∃ U(E). In the paper one answers affirmatively a question raised by B. Rodkin [K. F. Barth, D. A. Branna, and W. K. Hayman, "Research problems in complx analysis," Bull. London Math. Soc., l6, No. 5, 490-517, 1984]. Namely, one proves that in the family e{open}(d0) of continua E ∃ e{open}, satisfying the condition diam E=d0,o0≤2, one has the inequality {Mathematical expression} arcsin d0/2, one indicates all the cases for which equality prevails.
UR - http://www.scopus.com/inward/record.url?scp=0000365890&partnerID=8YFLogxK
U2 - 10.1007/BF01474448
DO - 10.1007/BF01474448
M3 - Article
AN - SCOPUS:0000365890
SN - 0090-4104
VL - 38
SP - 2140
EP - 2142
JO - Journal of Soviet Mathematics
JF - Journal of Soviet Mathematics
IS - 4
ER -