The present work draws on the understanding how notions of general potentialtheory - as set up, e.g., by Fuglede - explain existence and some basic resultson the "magical" rendezvous numbers. We aim at a fairly general description ofrendezvous numbers in a metric space by using systematically the potentialtheoretic approach. In particular, we generalize and explain results oninvariant measures, hypermetric spaces and maximal energy measures, whenshowing how more general proofs can be found to them.
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