Sharp inequalities relating volume and the min-max widths of Riemannian three-spheres
Analysis and Geometry Seminar
13th February 2020, 3:15 pm – 4:15 pm
The min-max theories for the area functional have undergone ground-breaking developments in recent years. One aspect of these theories is that they define many notions of "width" that can be regarded as geometric functionals on the space of Riemannian metrics on a given compact manifold. As such, it is an interesting question to understand how much geometric information these functionals contain about the Riemannian manifold. In this talk, we will focus on the Simon-Smith width of Riemannian three-dimensional spheres, and discuss how big can it be among metrics normalised to have the same volume. This is a joint project with Rafael Montezuma (UM-Amherst).