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4 papers · 1 filter
When Soap Bubbles Collide
Colin Adams, Frank Morgan, John M Sullivan
Can you fill R^n with a froth of "soap bubbles" that meet at most n at a time? Not if they have bounded diameter, as follows from Lebesgue's Covering Theorem. We provide some relat…
Coxeter Complexes and Graph-Associahedra
Michael Carr, Satyan L. Devadoss
Given a graph G, we construct a simple, convex polytope whose face poset is based on the connected subgraphs of G. This provides a natural generalization of the Stasheff associahed…
Quantum measurements and finite geometry
William K. Wootters
A complete set of mutually unbiased bases for a Hilbert space of dimension N is analogous in some respects to a certain finite geometric structure, namely, an affine plane. Another…
Regularity of area-minimizing surfaces in 3D polytopes and of invariant hypersurfaces in R^n
Frank Morgan
In (the surface of) a convex polytope P^3 in R^4, an area-minimizing surface avoids the vertices of P and crosses the edges orthogonally. In a smooth Riemannian manifold M with a g…