G-Ham Sandwich Theorems: Balancing measures by finite subgroups of spheres |
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Authors: | Steven Simon |
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Institution: | 1. The Courant Institute of Mathematical Sciences (New York University), 251 Mercer St., New York, NY 10012, United States;2. The Cooper Union for the Advancement of Science and Art, 41 Cooper Square, New York, NY 10003, United States |
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Abstract: | Equivariant Ham Sandwich Theorems are obtained for the classical algebras and the finite subgroups G of their unit spheres. Given any n -valued Borel measures on and any n-dimensional free -unitary representation of G, it is shown that there exists a Voronoi partition of naturally determined by G which “G-balances” each measure, as realized by the simultaneous vanishing of each “G-average” of the measures of the partition?s isometric fundamental domains. Applications for real measures follow, among them that any n signed mass distributions on can be equipartitioned by a single complex regular p-fan if p is an odd prime. |
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Keywords: | Equipartition |
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