The Converse Of The Archimedean Property of the Sphere and Related Results in Convex Geometry and Measure Theory

Geometry Topology Student Seminar
Wednesday, November 28, 2018 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Sidhanth Raman – Georgia Tech
Sudipta Kolay
The Archimedes Hatbox Theorem is a wonderful little theorem about the sphere and a circumscribed cylinder having the same surface area, but the sphere can potentially still be characterized by inverting the statement. There shall be a discussion of approaches to prove the claim so far, and a review of a weaker inversion of the Hatbox Theorem by Herbert Knothe and discussion of a related problem in measure theory that would imply the spheres uniqueness in this property.