14 citations · 31 across the 16 of their papers we have counts for
8 papers · 1 filter
The Space of Planar Soap Bubble Clusters
Frank Morgan
Soap bubbles and foams have been extensively studied by scientists, engineers, and mathematicians as models for organisms and materials, with applications ranging from extinguishin…
Isoperimetric Pentagonal Tilings
Ping Ngai Chung, Miguel A. Fernandez, Yifei Li +6
We identify least-perimeter unit-area tilings of the plane by convex pentagons, namely tilings by Cairo and Prismatic pentagons, find infinitely many, and prove that they minimize…
Existence of Least-perimeter Partitions
Frank Morgan
We prove the existence of a perimeter-minimizing partition of R^n into regions of unit volume. We conclude with a short tribute to the late Manuel A. Fortes.
In orbifolds, small isoperimetric regions are small balls
Frank Morgan
In a compact orbifold, for small prescribed volume, an isoperimetric region is close to a small metric ball; in a Euclidean orbifold, it is a small metric ball.
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…
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…