Estimates for conformal capacity



: Betsakos D., Vuorinen M.

: 2000

 Constructive Approximation

: 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.


Condenser, Conformal capacity, Elliptic integral, Green capacity, Hyperbolic metric, Polarization, Teichmüller's problem



Last updated on 26/11/2024 07:42:24 PM