Minimal surfaces are surfaces that locally minimize area, and they appear naturally in many geometric and physical contexts (such as soap films spanning wire frames). In this talk, we will explore a class of minimal surfaces called free boundary minimal surfaces (FBMS), which are surfaces inside the three-dimensional unit ball that locally minimize area while meeting the boundary sphere orthogonally.
These surfaces model, for example, equilibrium interfaces between two fluids inside a spherical container. They also arise variationally as critical points of the area functional under natural boundary constraints.
We will give an accessible introduction to the theory of FBMS, explain some of their key geometric properties, and describe a method for constructing such surfaces using equivariant min-max techniques.
