Let u(z,G) be the classical warping function of a simply connected domain G. We prove that the L p-norms of the warping function with different exponents are related by a sharp isoperimetric inequality, including the ...
Let u(x,G) be the stress function of a multiply connected plane domain G. We construct new domain functionals depending on this stress function which are isoperimetricallymonotone with respect to the free parameter. A ...