Condenser capacity and hyperbolic diameter

Given a compact connected set E in the unit disk B2, we give a new upper bound for the conformal capacity of the condenser (B2,E) in terms of the hyperbolic diameter t of E. Moreover, for t>0, we construct a set of hyperbolic diameter t and apply novel numerical methods to show that it has larger...

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Bibliographic Details
Main Author: Mohamed M.S., Nasser (author)
Other Authors: Rainio, Oona (author), Vuorinen, Matti (author)
Format: article
Published: 2021
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Online Access:http://dx.doi.org/10.1016/j.jmaa.2021.125870
https://www.sciencedirect.com/science/article/pii/S0022247X21009525
http://hdl.handle.net/10576/52959
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Summary:Given a compact connected set E in the unit disk B2, we give a new upper bound for the conformal capacity of the condenser (B2,E) in terms of the hyperbolic diameter t of E. Moreover, for t>0, we construct a set of hyperbolic diameter t and apply novel numerical methods to show that it has larger capacity than a hyperbolic disk with the same diameter. The set we construct is called a Reuleaux triangle in hyperbolic geometry and it has constant hyperbolic width equal to t.