Mario Schulz — Minimal surface exploration

Minimal surfaces, defined as critical points of the area functional, have intrigued scientists for centuries due to their geometric beauty and profound impact on the evolution of mathematical thought. Constructing embedded examples with prescribed topology is challenging, especially in ambient manifolds like the 3-sphere or the Euclidean unit ball, which only admit unstable minimal surfaces. We will introduce different avenues for existence results illustrated by visual examples and outline future directions of research.