Isoperimetric properties of condenser capacity

2020/10/19 by Nasser, Mohamed M. S., Vuorinen, Matti · 1 citation
#30C85 #31A15 #65E10 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.09704

Abstract

For compact subsets E of the unit disk \mathbbD we study the capacity of the condenser \rm cap( \mathbbD,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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• On computation of capacities and conformal invariants

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