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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| Format: | article |
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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. |
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