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arXiv · 2509.07224

Complete characterization of anisotropic geodesics in the Euclidean space

Pietro Aldrigo
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Abstract

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

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Pietro Aldrigo. 2025-09-08. Complete characterization of anisotropic geodesics in the Euclidean space. https://arxiv.org/abs/2509.07224

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