The Fermat–Torricelli Problem in Normed Planes and Spaces
By Horst Martini, K. Swanepoel, G. Weiss. 2002
80 citations recorded by the source corpus.
We investigate the Fermat–Torricelli problem in d-dimensional real normed spaces or Minkowski spaces, mainly for d=2. Our approach is to study the Fermat–Torricelli locus in a geometric way. We present many new results, as well as give an exposition of known results that are scattered in various sources, with proofs for some of them. Together, these results can be considered to be a minitheory of the Fermat–Torricelli problem in Minkowski spaces and especially in Minkowski planes. This demonstrates that substantial results about locational problems valid for all norms can be found using a geometric approach.
Subfields: Computational Mechanics, Geometry and Topology, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/61327b0ba1329aae0e8c5b3cf8094929a9d39eec
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In Computational Mechanics
In Geometry and Topology
Citations in the corpus
- The geometry of Minkowski spaces — A survey. Part I (2007, background): “A bounded closed subset S of a Minkowski plane is a Minkowski disc iff for any distinct x,y ∈ S there exists a semicircle in S with diameter [xy].”