## Isoperimetric inequality and capacity; Thomson's theorem on equilibrium potential

We investigate connections between mathematical potential theory and electrodynamics.

For example, we consider Thomson's theorem related to equilibrium potential from mathematical point of view and find motivation in physics for mathematical potential theory and vice versa. We also discuss versions of isoperimetric inequality related to capacity and electrostatic capacity. We consider inequalities between geometric quantities as perimeter, average diameter, area and capacity. In particular, we extend result that among all domains with given volume of the holes the domain bounded by two concentric spheres gives the smallest value $cap_F(K, D)$. Our investigation is also involved by connection between isoperimetric inequality, capacity, modulus of family of curves and Thomson's theorem related to equilibrium potential.

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