Natanael Alpay
Minimal Surfaces
Overview: Minimal surfaces are a topic in the study of differential geometry. Differential geometry has many applications and shows up in numerous places such as physics, engineering, and computer science. Abstract: A smooth n-dimensional manifold M is a topological space that locally has the same properties as the Euclidian space R^n, with smooth transition maps. A smooth surface is a two-dimensional manifold, for example, the sphere and the torus are such geometrical objects. In this presentation we will talk about minimal surfaces which locally minimize the area function. We will show that this is equivalent to the fact that mean curvature of the surface is zero. An obvious example is the Euclidean plane, where the curvature is zero everywhere, but we will show a plethora of such surfaces such as the catenoid, the helicoid, Dinii surfaces, Enneper surfaces, and many more. Apart from their beauty, these minimal surfaces have applications in material science, architecture, etc.
Zoom Link