THE MODULUS OF THE KORÁNYI ELLIPSOIDAL RING.

The Korányi ellipsoidal ring ε = εB,A, 0 < B < A, is defined as the image of the Korányi spherical ring centred at the origin and of radii B and A via a linear contact quasiconformal map L in the Heisenberg group. If K ≥ 1 is the maximal distortion of L, then we prove that the modulus of ε is equal to mod(ε) = (3/8(K²+1/K²)+1/4)π²/(log(A/B))³. [ABSTRACT FROM AUTHOR]