Busemann Functionals

Busemann functionals are mathematical tools used in geometry to analyze the shape and structure of spaces, particularly in the study of geometric boundaries called "horospheres." They measure how far a point is along a specific "direction at infinity," associated with a given path heading towards the boundary. Think of them as functions that assign a real number to each point, indicating its relative position as you travel towards a boundary point at infinity. This concept helps mathematicians understand the large-scale geometry and asymptotic behavior of complex spaces, especially in the context of non-Euclidean and metric geometries.