Gergen Lecture #2
Friday, November 18, 2016, 4:00pm, Physics 119
Simon Brendle (Columbia University)
Minimal surfaces in S^3 and the Lawson conjecture

Abstract:

A central problem in minimal surface theory is to understand minimal surfaces in spheres (or, equivalently, minimal cones in Euclidean space). The most basic examples of minimal surfaces in the three-dimensional sphere S^3 are the equator and the Clifford torus. Moreover, there is an abundance of minimal surfaces in S^3 of higher genus; the first examples were found by Lawson. In 1966, Almgren gave a complete classification of all minimal surfaces in S^3 of genus 0: the equator is the only example up to ambient isometries. In 1969, Lawson conjectured that, up to ambient isometries, the Clifford torus is the only minimal surface of genus 1 which is embedded (i.e. free of self-intersections). In this lecture, I will discuss the proof of Lawson's conjecture.

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