14 citations · 31 across the 16 of their papers we have counts for
17 papers
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…
Are large two-dimensional clusters of perimeter-minimizing bubbles of equal-area hexagonal or circular?
S. J. Cox, F. Morgan, F. Graner
A computer study of clusters of up to 200,000 equal-area bubbles shows for the first time that rounding conjectured optimal hexagonal planar soap bubble clusters reduces perimeter.
The Isoperimetric Problem in Higher Codimension
Frank Morgan, Isabel M. C. Salavessa
We consider three generalizations of the isoperimetric problem to higher codimension and provide results on equilibrium, stability, and minimization.
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 isoperimetric regions in with density
Frank Morgan, Aldo Pratelli
We prove the existence of isoperimetric regions in with density under various hypotheses on the growth of the density. Along the way we prove results on the boundedness of i…
Steiner and Schwarz symmetrization in warped products and fiber bundles with density
Frank Morgan, Sean Howe, Nate Harman
We provide very general symmetrization theorems in arbitrary dimension and codimension, in products, warped products, and certain fiber bundles such as lens spaces, including Stein…