Gap Theorems for Minimal Submanifolds of Spheres
Channel: UMD Mathematics
Date: 2013-04-23

Brian White
Professor of Mathematics
Stanford University

ABSTRACT
The totally geodesic k-sphere is the minimal hypersurface in the (k+1)-sphere of smallest k-dimensional area. What is the next smallest area? This is closely related to the question: what is the smallest density that a minimal variety can have at a singular point? I will discuss these questions and some sharp partial results.

Recorded April 12, 2013 as part of Calabifest: The 28th Geometry Festival.