Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 182, Pages 33–38
DOI: https://doi.org/10.36535/0233-6723-2020-182-33-38 (Mi into670) 		 
Hausdorff realization of linear geodesics in the Gromov–Hausdorff space

A. O. Ivanov, A. A. Tuzhilin

Lomonosov Moscow State University
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DOI: https://doi.org/10.36535/0233-6723-2020-182-33-38
Abstract: A realization of a “rectilinear” geodesic lying in the Gromov–Hausdorff space is constructed in the form of the shortest geodesic with respect to the Hausdorff distance in some ambient metric space.
Keywords: metric geometry, Hausdorff distance, Gromov–Hausdorff distance, geodesic.
Funding agency Grant number
Grant of the President of the Russian Federation НШ-6399.2018.1
19-01-00775-a
This work was supported by the program of the President of the Russian Federation for the leading scientific schools of Russia (project NSh-6399.2018.1, agreement 075-02-2018-867) and the Russian Foundation for Basic Research (project No. 19-01-00775-a).
Bibliographic databases:
Document Type: Article
UDC: 514.75
MSC: 51F99, 53C23
Language: Russian
Citation: A. O. Ivanov, A. A. Tuzhilin, “Hausdorff realization of linear geodesics in the Gromov–Hausdorff space”, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 182, VINITI, Moscow, 2020, 33–38
Citation in format AMSBIB
\Bibitem{IvaTuz20}
\by A.~O.~Ivanov, A.~A.~Tuzhilin
\paper Hausdorff realization of linear geodesics in the Gromov--Hausdorff space
\inbook Proceedings of the International Conference "Classical and Modern Geometry"
Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev.
Moscow, April 22-25, 2019. Part 4
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 182
\pages 33--38
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into670}
\crossref{https://doi.org/10.36535/0233-6723-2020-182-33-38}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4208398}
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