Harmonic measure on an annulus
J. A. Hummel, Bernard Pinchuk · Complex Variables Theory and Application An International Journal · 1993
Gaier's problem is to find a continuum in the closed unit disc which contains two given points a and b so as to minimize ω(0) where ω(z) is the harmonic measure of Ω in the unit disc. A variational method is used m derive the differential equation for the extremal case of this problem. A special transformation simplifies the analysis of the problem in the symmetric case