Strategy-proof location of a public bad on a disc

In a model with finitely many agents who have single-dipped Euclidean preferences on a disc in the Euclidean plane, a rule assigns to each profile of reported dips a point of the disc. It is proved that any strategy-proof and Pareto optimal rule is a dictatorial. This framework models situations where public bads such as garbage dumping grounds or nuclear plants have to be located within a confined region that has the shape of a disc.