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Russian Mathematical Surveys, 2012, Volume 67, Issue 5, Pages 785–890
DOI: https://doi.org/10.1070/RM2012v067n05ABEH004808 (Mi rm9490) 		 
This article is cited in 136 scientific papers (total in 137 papers)

The Monge–Kantorovich problem: achievements, connections, and perspectives

V. I. Bogachevab, A. V. Kolesnikovc

a M. V. Lomonosov Moscow State University
b St. Tikhon's Orthodox University
c Higher School of Economics
English version PDF (1291 kB) Citations (137) Russian version article
References:
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DOI: https://doi.org/10.1070/RM2012v067n05ABEH004808
Abstract: This article gives a survey of recent research related to the Monge–Kantorovich problem. Principle results are presented on the existence of solutions and their properties both in the Monge optimal transportation problem and the Kantorovich optimal plan problem, along with results on the connections between both problems and the cases when they are equivalent. Diverse applications of these problems in non-linear analysis, probability theory, and differential geometry are discussed.
Bibliography: 196 titles.
Keywords: Monge problem, Kantorovich problem, optimal transportation, transport inequality, Kantorovich–Rubinshtein metric.
Received: 20.06.2012
Bibliographic databases:
Document Type: Article
UDC: 519.2+517.9
MSC: 28C20, 35J96, 49Q20, 60B05
Language: English
Original paper language: Russian
Citation: V. I. Bogachev, A. V. Kolesnikov, “The Monge–Kantorovich problem: achievements, connections, and perspectives”, Russian Math. Surveys, 67:5 (2012), 785–890
Citation in format AMSBIB
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\by V.~I.~Bogachev, A.~V.~Kolesnikov
\paper The Monge--Kantorovich problem: achievements, connections, and perspectives
\jour Russian Math. Surveys
\yr 2012
\vol 67
\issue 5
\pages 785--890
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  • https://doi.org/10.1070/RM2012v067n05ABEH004808
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    • This publication is cited in the following 137 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:4040
    Russian version PDF:2338
    English version PDF:194
    References:195
    First page:136
     
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