Condenser capacity and hyperbolic diameter




Nasser Mohamed MS, Rainio Oona, Vuorinen Matti

PublisherElsevier

2022

Journal of Mathematical Analysis and Applications

125870

508

1

1096-0813

DOIhttps://doi.org/10.1016/j.jmaa.2021.125870

https://doi.org/10.1016/j.jmaa.2021.125870

https://research.utu.fi/converis/portal/detail/Publication/174813662



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.


Last updated on 2024-26-11 at 19:42