A1 Refereed original research article in a scientific journal
Estimates for conformal capacity
Authors: Betsakos D., Vuorinen M.
Publication year: 2000
Journal: Constructive Approximation
Journal name in source: Constructive Approximation
Volume: 16
Issue: 4
First page : 589
Last page: 602
Number of pages: 14
ISSN: 0176-4276
Web address : http://api.elsevier.com/content/abstract/scopus_id:0034337995
Abstract
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.
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.
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