For Finsler metrics with bi-geodesics, the arithmetic and maximum symmetrisations of the distance are shown to be Finsler, with explicit Lagrangians, generalising known Hilbert and Funk results.
Busemann, The geometry of Finsler spaces
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On families of Finsler metrics
For Finsler metrics with bi-geodesics, the arithmetic and maximum symmetrisations of the distance are shown to be Finsler, with explicit Lagrangians, generalising known Hilbert and Funk results.