1 citations · 2 across the 5 of their papers we have counts for
Showing math.MGShow all
3 papers · 1 filter
math.MG2004
Planar Clusters
Aladar Heppes, Frank Morgan
We provide upper and lower bounds on the least-perimeter way to enclose and separate n regions of equal area in the plane. Along the way, inside the hexagonal honeycomb, we provide…
math.MG2004★ 1 cited
Hexagonal surfaces of Kapouleas
Frank Morgan
For the "hexagonal" norm on R^3, for which the isoperimetric shape is a hexagonal prism rather than a round ball, we give analogs of the compact immersed constant-mean-curvature su…
math.MG2004
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…