A. V. Akopyan, A. S. Tarasov, “A Constructive Proof of Kirszbraun's Theorem”, Mat. Zametki, 84:5 (2008), 781–784; Math. Notes, 84:5 (2008), 725

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Matematicheskie Zametki, 2008, Volume 84, Issue 5, Pages 781–784
DOI: https://doi.org/10.4213/mzm4438 (Mi mzm4438)

This article is cited in 15 scientific papers (total in 15 papers)

Brief Communications

A Constructive Proof of Kirszbraun's Theorem

A. V. Akopyan, A. S. Tarasov

Institute of Systems Analysis, Russian Academy of Sciences

Full-text PDF (318 kB) Citations (15)

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DOI: https://doi.org/10.4213/mzm4438

Keywords:

P L

$PL$ -isometry, weakly contractive map, extension of maps, Kirszbraun's theorem, Helly's theorem, separable space.

Received: 05.02.2008

English version:
Mathematical Notes, 2008, Volume 84, Issue 5, Pages 725–728
DOI: https://doi.org/10.1134/S000143460811014X

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: A. V. Akopyan, A. S. Tarasov, “A Constructive Proof of Kirszbraun's Theorem”, Mat. Zametki, 84:5 (2008), 781–784; Math. Notes, 84:5 (2008), 725–728

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm4438

https://doi.org/10.4213/mzm4438

https://www.mathnet.ru/eng/mzm/v84/i5/p781

This publication is cited in the following 15 articles:

Osinenko P., “Towards a Constructive Framework For Control Theory”, IEEE Control Syst. Lett., 6 (2022), 379–384
Ciosmak K.J., “Continuity of Extensions of Lipschitz Maps”, Isr. J. Math., 245:2 (2021), 567–588
Azagra D., Le Gruyer E., Mudarra C., “Kirszbraun'S Theorem Via An Explicit Formula”, Can. Math. Bul.-Bul. Can. Math., 64:1 (2021), 142–153
Sharf M., “On the Sample Complexity of Data-Driven Inference of the l-2-Gain”, IEEE Control Syst. Lett., 4:4 (2020), 904–909
Musin O.R., “Graphs and Spherical Two-Distance Sets”, Eur. J. Comb., 80 (2019), 311–325
Chandgotia N., Pak I., Tassy M., “Kirszbraun-Type Theorems For Graphs”, J. Comb. Theory Ser. B, 137 (2019), 10–24
Cobzas S., Miculescu R., Nicolae A., “Lipschitz Functions Preface”: Cobzas, S Miculescu, R Nicolae, A, Lipschitz Functions, Lect. Notes Math., Lecture Notes in Mathematics, 2241, Springer International Publishing Ag, 2019, V+
Ştefan Cobzaş, Radu Miculescu, Adriana Nicolae, Lecture Notes in Mathematics, 2241, Lipschitz Functions, 2019, 211
Gorbovickis I., “The Central Set and Its Application to the Kneser-Poulsen Conjecture”, Discret. Comput. Geom., 59:4 (2018), 784–801
Mahabadi S., Makarychev K., Makarychev Yu., Razenshteyn I., “Nonlinear Dimension Reduction Via Outer Bi-Lipschitz Extensions”, Stoc'18: Proceedings of the 50Th Annual Acm Sigact Symposium on Theory of Computing, eds. Diakonikolas I., Kempe D., Henzinger M., Assoc Computing Machinery, 2018, 1088–1101
Osinenko P., Streif S., “A Constructive Version of the Extremum Value Theorem For Spaces of Vector-Valued Functions”, J. Log. Anal., 10 (2018), 4
Kupavskii A.B., Polyanskii A., “Proof of Schur'S Conjecture in R-D”, Combinatorica, 37:6 (2017), 1181–1205
A. Petrunin, A. Yashinski, “Piecewise distance preserving maps”, St. Petersburg Math. J., 27:1 (2016), 155–175
Wu Y., Verdú S., “Optimal phase transitions in compressed sensing”, IEEE Trans. Inform. Theory, 58:10 (2012), 6241–6263
A. Petrunin, “On intrinsic isometries to Euclidean space”, St. Petersburg Math. J., 22:5 (2011), 803–812

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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