14 citations · 31 across the 16 of their papers we have counts for
7 papers · 1 filter
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.
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…
Stable constant mean curvature hypersurfaces are area minimizing in small L^1 neighborhoods
Frank Morgan, Antonio Ros
We prove that a strictly stable constant-mean-curvature hypersurface in a smooth manifold of dimension less than or equal to 7 is uniquely homologically area minimizing for fixed v…
The Levy-Gromov Isoperimetric Inequality in Convex Manifolds with Boundary
Frank Morgan
We observe after Bayle and Rosales that the Levy-Gromov isoperimetric inequality generalizes to convex manifolds with boundary.
On the isoperimetric problem in Euclidean space with density
César Rosales, Antonio Cañete, Vincent Bayle +1
We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher…
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…