Estimates for conformal capacity

: Betsakos D., Vuorinen M.

: 2000

: Constructive Approximation

: 16

: 4

: 589

: 602

: 14

: 0176-4276

: http://api.elsevier.com/content/abstract/scopus_id:0034337995

Let a, b, c, d be distinct points on R̄ . By p we denote the minimal conformal capacity of all rings (E, F) with a, b ∈ E and c, d ∈ F. For n = 2, we use explicit expressions of p in terms of complete elliptic integrals to prove a sharp inequality that connects p and the conformal capacity of Teichmüller's ring. We also show, by a concrete example, how we can use techniques involving polarization and hyperbolic geometry to prove estimates for the conformal capacity of rings.