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CORR
2008
Springer
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13 years 11 months ago
An optimization problem on the sphere
We prove existence and uniqueness of the minimizer for the average geodesic distance to the points of a geodesically convex set on the sphere. This implies a corresponding existen...
Andreas Maurer
JCDCG
1998
Springer
14 years 3 months ago
Radial Perfect Partitions of Convex Sets in the Plane
In this paper we study the following problem: how to divide a cake among the children attending a birthday party such that all the children get the same amount of cake and the same...
Jin Akiyama, Atsushi Kaneko, Mikio Kano, Gisaku Na...
FSTTCS
2004
Springer
14 years 4 months ago
Testing Geometric Convexity
We consider the problem of determining whether a given set S in Rn is approximately convex, i.e., if there is a convex set K ∈ Rn such that the volume of their symmetric differe...
Luis Rademacher, Santosh Vempala