In this article we formulate several conjectures concerning the lowest
eigenvalue of a Dirac operator with an external electrostatic potential. The
latter describes a relativistic quantum electron moving in the field of some
(pointwise or extended) nuclei. The main question we ask is whether the
eigenvalue is minimal when the nuclear charge is concentrated at one single
point. This well-known property in nonrelativistic quantum mechanics has
escaped all attempts of proof in the relativistic case.

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