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تسجيل مستخدم جديدIsoperimetric properties of condenser capacity
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For compact subsets $E$ of the unit disk $ mathbb{D}$ we study the capacity of the condenser ${rm cap}( mathbb{D},E)$ 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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