EVENT DETAILS AND ABSTRACT

Title: Yamabe Lecture 2: Minimal surfaces and the Willmore Conjecture
Speaker: Fernando Codá Marques
Speaker Info: IMPA
Brief Description:
Special Note:
Abstract:

In 1965, T. J. Willmore conjectured that the integral of the square of the mean curvature of any torus immersed in Euclidean three-space is at least 2\pi^2. In this series of three lectures we will describe a proof of this conjecture that uses the min-max theory of minimal surfaces. This is joint work with Andre Neves.

In this lecture we will construct and analyze the geometric and topological properties of the canonical family: a specific five-dimensional family of deformations of a surface in the three-sphere that keeps the area bounded above by the Willmore energy. We will derive a key degree calculation that explains how the information about the genus of the surface comes into play.