= Constrained electrostatic equilibrium
A particle constrained to a surface can have a stable minimum of <electrostatic potential> restricted to that surface even when the unrestricted equilibrium is unstable. Away from source charges, <Laplace's equation> makes the full potential <Hessian matrix> trace zero, which rules out a positive-definite three-dimensional Hessian but does not rule out a positive-definite restriction to two dimensions. Equal positive charges at the corners of a square give a planar minimum at its centre and an unstable perpendicular direction.
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