The log-ratio distance on unit-area triangles is a complete Finsler metric of Thompson type; its geodesic, Finsler, and completeness structure extends to triangulated Euclidean surfaces, with an example showing forward incompleteness there.
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On spaces of Euclidean triangles and triangulated Euclidean surfaces
The log-ratio distance on unit-area triangles is a complete Finsler metric of Thompson type; its geodesic, Finsler, and completeness structure extends to triangulated Euclidean surfaces, with an example showing forward incompleteness there.