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arXiv · 2010.09704

Isoperimetric properties of condenser capacity

Mohamed M. S. Nasser·Matti Vuorinen
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Abstract

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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Mohamed M. S. Nasser, Matti Vuorinen. 2020-10-19. Isoperimetric properties of condenser capacity. https://arxiv.org/abs/2010.09704

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