Geometry Seminar: P. McGrath (NCSU)

Geometry Seminar (Geometric Analysis)

Speaker: Peter McGrath (NCSU)

Title: Areas for genus zero free boundary minimal surfaces in the ball

Abstract: A free boundary minimal surface (FBMS) in the unit Euclidean 3-ball is a minimal surface whose boundary meets the unit sphere orthogonally.  Such surfaces are critical points for the area functional among variations of the ball which preserve its boundary as a set.  In surprising recent work, several authors have constructed sequences genus zero FBMS which converge to the unit sphere in the sense of varifolds.  We show that the area of any genus zero FBMS is bounded above by $4\pi$, and show that the only way this inequality can be asymptotically achieved is by a sequence of surfaces converging to the sphere in the sense of varifolds. This is joint work with Jiahua Zou.