Busemann Functions

Busemann functions are mathematical tools used mainly in convex geometry and optimization. They help describe the geometry of shapes, particularly when analyzing their boundaries and faces. Specifically, a Busemann function is associated with a direction in space and provides a way to measure distances in a manner that focuses on the "far away" points of a shape. In essence, these functions facilitate the understanding of how certain geometric structures behave and can be used to solve problems related to shape optimization and analysis in mathematics and related fields.