Geodesic
Action of similarity transformations on families of metric spaces
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. 3-13.

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We study the action of the multiplicative group of positive real numbers on various families of a metric space, which consists of multiplying all distances in the metric space by the same positive real number; such an action is called similarity. Stationary subgroups of such actions are studied.
Keywords: metric geometry, Gromov–Hausdorff distance, Gromov–Hausdorff eigenclass, cloud, similarity group action. 
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S. A. Bogatyi; A. A. Tuzhilin. Action of similarity transformations on families of metric spaces. 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. 3-13. http://geodesic.mathdoc.fr/item/INTO_2023_223_a0/

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