The Isoperimetric Problem with Density
Frank Morgan, Williams College, presents their seminar.
About the Seminar
The Ancient Greeks proved the circle the least-perimeter enclosure of given area. For thousands of years new versions of this "isoperimetric problem" have had applications throughout mathematics and beyond. Recent applications, including Perelman's proof of the Poincaré Conjecture, require that the ambient space carry a density that weights both perimeter and area. We discuss some open problems and recent results, some by undergraduates. No prerequisites, students welcome.