Complete characterization of anisotropic geodesics in the Euclidean space

Abstract We provide a characterization of absolutely continuous paths that minimize the anisotropic F –length between two points, where F is a lower semi–continuous, 1–homogeneous positive function defined on $${\mathbb {R}^{n}}$$ R n . The characterization is achieved by establishing a connection between the minimizing paths and the geometry of the anisotropic F –isoperimetric set.