1 citations · 2 across the 5 of their papers we have counts for
5 papers
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…
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…
Proof of the Double Bubble Conjecture
Michael Hutchings, Frank Morgan, Manuel Ritoré +1
We prove that the standard double bubble provides the least-area way to enclose and separate two regions of prescribed volume in \Bbb R^3.
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…
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…