Isoperimetric properties of condenser capacity

Isoperimetric properties of condenser capacity

For compact subsets E of the unit disk D we study the capacity of the condenser (D,E) by means of set functionals defined in terms of hyperbolic geometry. In particular, we study experimentally the case of a hyperbolic triangle and arrive at the conjecture that of all triangles with the same hyperbo...

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Veröffentlicht in:Journal of mathematical analysis and applications 2021-07, Vol.499 (1), p.125050, Article 125050
Hauptverfasser: Nasser, Mohamed M.S., Vuorinen, Matti
Format: Artikel
Sprache:eng
Schlagworte:
Boundary integral equation
Condenser capacity
Hyperbolic metric
Isoperimetric problems
Numerical computation
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Zusammenfassung:For compact subsets E of the unit disk D we study the capacity of the condenser (D,E) by means of set functionals defined in terms of hyperbolic geometry. In particular, we study experimentally the case of a hyperbolic triangle and arrive at the conjecture that of all triangles with the same hyperbolic area, the equilateral triangle has the least capacity.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.125050