TY - JOUR

T1 - Minimization of the conformal radius under circular cutting of a domain

AU - Solynin, A. Yu

PY - 2001

Y1 - 2001

N2 - Let D be a simply connected domain on the complex plane such that 0 ∈ D. For r > 0, let Dr be the connected component of D ∩ z: |z| < r containing the origin. For fixed r, we solve the problem on minimization of the conformal radius R(Dr, 0) among all domains D with given conformal radius R(D, 0). This also leads to the solution of the problem on maximization of the logarithmic capacity of the local ε-extension Eε(a) of E among all continua E with given logarithmic capacity. Here, Eε(a) = E ∪ z: |z-a| ≤ ε, α ∈ E, ε > 0.

AB - Let D be a simply connected domain on the complex plane such that 0 ∈ D. For r > 0, let Dr be the connected component of D ∩ z: |z| < r containing the origin. For fixed r, we solve the problem on minimization of the conformal radius R(Dr, 0) among all domains D with given conformal radius R(D, 0). This also leads to the solution of the problem on maximization of the logarithmic capacity of the local ε-extension Eε(a) of E among all continua E with given logarithmic capacity. Here, Eε(a) = E ∪ z: |z-a| ≤ ε, α ∈ E, ε > 0.

UR - http://www.scopus.com/inward/record.url?scp=52549111654&partnerID=8YFLogxK

U2 - 10.1023/A:1011337310404

DO - 10.1023/A:1011337310404

M3 - Article

AN - SCOPUS:52549111654

VL - 105

SP - 2220

EP - 2234

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

M1 - 341655

ER -