Rasmus Johansen Jouttijärvi - An introduction to index theory for complete minimal surfaces

Why are some leaves saddle shaped? and why are planets generally spherical? The study of minimal surfaces can help us understand many of the shapes we find in nature, and it may allow us to ask even deeper questions about those shapes. 

In this talk we provide a brief introduction to the topic of minimal surfaces in 3D-space, and we try to answer the question of whether or not the surfaces are truly minimal. This involves ascribing each surface an "index of stability", which is intimately related to the curvature of the surface. We show how the interplay between curvature and index allow us to categorize all complete minimal surfaces up to index 4.