caa a22 4500 445835508 CHVBK 20180317145329.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00209-010-0700-y doi (NATIONALLICENCE)springer-10.1007/s00209-010-0700-y A note on the metric geometry of the unit ball [Elektronische Daten] [Aicke Hinrichs, Peter Nickolas, Reinhard Wolf] Denote by B n the unit ball in the Euclidean space $${\mathbb{R}^n}$$ and define $$ M(B^n) = \sup \int_{B^n} \int_{B^n}\| x - y \| \, d\mu(x)d\mu(y),$$ where the supremum is taken over all finite signed Borel measuresμ on B n of total mass 1. In this paper, the value of M(B n ) is computed explicitly for all n, and it is shown that for n > 1 no measure exists that achieves the supremum defining M(B n ). These results generalize the work of Alexander (Proc Am Math Soc 64:317-320, 1977) on M(B 3). Springer-Verlag, 2010 Euclidean unit ball nationallicence Compact metric space nationallicence Signed Borel measure nationallicence Spaces of Borel measures nationallicence Metric geometry nationallicence Distance geometry nationallicence Geometric constant nationallicence Hinrichs Aicke Mathematisches Institut, Universität Jena, Ernst-Abbe-Platz 2, 07740, Jena, Germany aut Nickolas Peter School of Mathematics and Applied Statistics, University of Wollongong, 2522, Wollongong, NSW, Australia aut Wolf Reinhard Institut für Mathematik, Universität Salzburg, Hellbrunnerstrasse 34, 5020, Salzburg, Austria aut Mathematische Zeitschrift Springer-Verlag 268/3-4(2011-08-01), 887-896 0025-5874 268:3-4<887 2011 268 209 https://doi.org/10.1007/s00209-010-0700-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0700-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hinrichs Aicke Mathematisches Institut, Universität Jena, Ernst-Abbe-Platz 2, 07740, Jena, Germany aut NATIONALLICENCE 700 1- Nickolas Peter School of Mathematics and Applied Statistics, University of Wollongong, 2522, Wollongong, NSW, Australia aut NATIONALLICENCE 700 1- Wolf Reinhard Institut für Mathematik, Universität Salzburg, Hellbrunnerstrasse 34, 5020, Salzburg, Austria aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/3-4(2011-08-01), 887-896 0025-5874 268:3-4<887 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer