1955/12/01 by Kurt Strebel · 2 citations
Mathematics · #Analytic and geometric function theory
paper · pdf · doi:10.1090/s0002-9939-1955-0073702-x
openalex publication_date 1955/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/03/11
1. Let G and G' be two plane open sets and w(z) a topological mapping of G onto G'. By Q we denote any quadrilateral in G, i.e. the topological image of a closed square with a distinguished pair of opposite sides. The conformal modulus m of Q is the ratio m = a/b of the sides of a conformally equivalent rectangle R, the distinguished sides of Q corresponding to the sides of length b. We call this essentially unique conformal mapping of Q onto R the canonical mapping of Q. The modulus m is equal to the extremal distance of the two distinguished sides of Q with respect to Q. The maximal dilation of the mapping w(z) on G is the number