Geodesic
Deforming Minkowski norms to Euclidean norms
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Tome 223 (2023), pp. 107-111

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We study deformations of Minkowski norms with piecewise smooth indicatrices determined by linearly independent $1$-forms and a piecewise smooth positive function. Such a deformation of the Euclidean norm generalizes the classical $(\alpha,\beta)$-norms by M. Matsumoto. We show that any Minkowski norm can be deformed into a Euclidean norm by a composition of such deformations.
Keywords: сonvex body, Minkowski norm. 
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     title = {Deforming {Minkowski} norms to {Euclidean} norms},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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V. Yu. Rovenskiǐ. Deforming Minkowski norms to Euclidean norms. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Tome 223 (2023), pp. 107-111. http://geodesic.mathdoc.fr/item/INTO_2023_223_a9/