Potential Theoretic Approach to Rendezvous Numbers |
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Authors: | Bálint Farkas Szilárd Gy Révész |
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Institution: | Technische Universit?t Darmstadt, Germany Hungarian Academy of Sciences, Budapest, Hungary
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Abstract: | We analyze relations between various forms of energies (reciprocal capacities), the transfinite diameter, various Chebyshev
constants and the so-called rendezvous or average number. The latter is originally defined for compact connected metric spaces
(X,d) as the (in this case unique) nonnegative real number r with the property that for arbitrary finite point systems {x
1, …, x
n
} ⊂ X, there exists some point x ∈ X with the average of the distances d(x,x
j
) being exactly r. Existence of such a miraculous number has fascinated many people; its normalized version was even named “the magic number”
of the metric space. Exploring related notions of general potential theory, as set up, e.g., in the fundamental works of Fuglede
and Ohtsuka, we present an alternative, potential theoretic approach to rendezvous numbers. |
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Keywords: | 2000 Mathematics Subject Classifications: 31C15 28A12 54D45 46B20 |
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