caa a22 4500 475743717 CHVBK 20180406123506.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1007/s003650010002 doi (NATIONALLICENCE)springer-10.1007/s003650010002 Estimates for conformal capacity [Elektronische Daten] [D. Betsakos, M. Vuorinen] Abstract. : Let a,b,c,d be distinct points on \overline \bf R n . 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. Springer-Verlag New York, 2000 Key words. Condenser, Conformal capacity, Green capacity, Elliptic integral, Teichmüller's problem, Hyperbolic metric, Polarization. AMS Classification. Primary: 30C85, 30C75. Secondary: 31B15 nationallicence Betsakos D. Department of Mathematics, betsakos@geom.helsinki.fi, University of Helsinki FIN-00014 Finland, P.O. Box 4, FI aut Vuorinen M. Department of Mathematics, vuorinen@csc.fi, University of Helsinki FIN-00014 Finland, P.O. Box 4, FI aut https://doi.org/10.1007/s003650010002 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003650010002 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Betsakos D. Department of Mathematics, betsakos@geom.helsinki.fi, University of Helsinki FIN-00014 Finland, P.O. Box 4, FI aut NATIONALLICENCE 700 1- Vuorinen M. Department of Mathematics, vuorinen@csc.fi, University of Helsinki FIN-00014 Finland, P.O. Box 4, FI aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer