Points on Hemispheres

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dc.creatorFricke, Jan
dc.date2006-10-04
dc.date2006-10-23
dc.date.accessioned2026-07-07T07:28:41Z
dc.date.available2026-07-07T07:28:41Z
dc.descriptionWe will show that for any $n\ge N$ points on the $N$-dimensional sphere $S^N$ there is a closed hemisphere which contains at least $\lfloor\frac{n+N+1}{2}\rfloor$ of these points. This bound is sharp and we will calculate the amount of sets which realize this value. If we change to open hemispheres things will be easier. For any $n$ points on the sphere there is an open hemisphere which contains at least $\lfloor\frac{n+1}{2}\rfloor$ of these points, independent of the dimension. This bound is sharp.
dc.identifierhttps://arxiv.org/abs/math/0610140
dc.identifierhttp://arxiv.org/abs/math/0610140
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117825
dc.subjectMetric Geometry
dc.subjectProbability
dc.subject51F99 ;60D05
dc.titlePoints on Hemispheres
dc.typetext

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