## Electrostatic characterization of spheres.(English)Zbl 0948.31004

The classical results on the distribution of electrostatic charge in a three-dimensional Euclidean space go back to Gauss. A property of a closed sphere is that the charge is uniformly distributed on its surface. The authors prove that a sphere in $$\mathbb{R}^{n}, n\geq 2$$, is the only surface boundary of convex bodies for which electric charges distribute uniformly (with a constant density) in the absence of exterior fields.

### MSC:

 31B15 Potentials and capacities, extremal length and related notions in higher dimensions 78A30 Electro- and magnetostatics 52A20 Convex sets in $$n$$ dimensions (including convex hypersurfaces) 32J25 Transcendental methods of algebraic geometry (complex-analytic aspects)

### Keywords:

single-layer potential; charge distribution; convex bodies
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### References:

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