10 citations · 34 across the 13 of their papers we have counts for
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math.MG2013
Moser's Shadow Problem
Jeffrey C. Lagarias, Yusheng Luo, Arnau Padrol
Moser's shadow problem asks to estimate the shadow function , which is the largest number such that for each bounded convex polyhedron with vertices in $…
math.MG2013
Weakly Circle-Preserving Maps in Inversive Geometry
Joel C. Gibbons, Yusheng Luo
Let S^n be the standard n-sphere embedded in R^{n+1}. A mapping T: S^n \to S^n, not assumed continuous or even measurable, nor injective, is called weakly circle-preserving if the…
math.MG2013★ 1 cited
Colorings of the n-sphere and inversive geometry
Joel C. Gibbons, Yusheng Luo
This paper shows that in dimensions n \geq 2 for any partition of the set of points in the standard n-sphere \sum_{i=0}^n x_i^2 =1 in R^{n+1} into (n+3) or more nonempty sets, ther…