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 hyperbolic area, the equilateral triangle has the least capacity.

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Published in: Journal of Mathematical Analysis and Applications
License: http://creativecommons.org/licenses/by/4.0/
See article on publisher's website: https://dx.doi.org/10.1016/j.jmaa.2021.125050