40 citations · 186 across the 33 of their papers we have counts for
5 papers · 1 filter
Isoperimetric Regions in Nonpositively Curved Manifolds
Joel Hass
Isoperimetric regions minimize the size of their boundaries among all regions with the same volume. In Euclidean and Hyperbolic space, isoperimetric regions are round balls. We sho…
Minimal Fibrations of Hyperbolic 3-manifolds
Joel Hass
There are hyperbolic 3-manifolds that fiber over the circle but that do not admit fibrations by minimal surfaces. Furthermore these manifolds do not admit fibrations by surfaces th…
A Metric for genus-zero surfaces
Joel Hass, Patrice Koehl
We present a new method to compare the shapes of genus-zero surfaces. We introduce a measure of mutual stretching, the symmetric distortion energy, and establish the existence of a…
Area Inequalities for Embedded Disks Spanning Unknotted Curves
Joel Hass, Jeffrey C. Lagarias, William P. Thurston
We show that a smooth unknotted curve in R^3 satisfies an isoperimetric inequality that bounds the area of an embedded disk spanning the curve in terms of two parameters: the lengt…
Double Bubbles Minimize
Joel Hass, Roger Schlafly
The classical isoperimetric inequality in R^3 states that the surface of smallest area enclosing a given volume is a sphere. We show that the least area surface enclosing two equal…