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Uspekhi Mat. Nauk, 2011, Volume 66, Issue 4(400), Pages 103–136 (Mi umn9429)  

This article is cited in 3 scientific papers (total in 3 papers)

Theory of fields of extremals for multiple integrals

M. I. Zelikinab

a Moscow State University
b Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: A general theory unifying and generalizing the field theories for multiple integrals due to Weyl and Carathéodory is developed. Generalizations of the Legendre, Weyl, and Carathéodory transforms are introduced, as well as the associated connection and curvature on the fibre bundle underlying the multiple integrals.
Bibliography: 33 titles.

Keywords: field of extremals, Weierstrass function, Legendre transform, connection and curvature on fibre bundles, covariant differentiation.

DOI: https://doi.org/10.4213/rm9429

Full text: PDF file (700 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2011, 66:4, 733–765

Bibliographic databases:

UDC: 517.972
MSC: 34A26, 49K20, 58E15
Received: 14.09.2010

Citation: M. I. Zelikin, “Theory of fields of extremals for multiple integrals”, Uspekhi Mat. Nauk, 66:4(400) (2011), 103–136; Russian Math. Surveys, 66:4 (2011), 733–765

Citation in format AMSBIB
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Linking options:
  • http://mi.mathnet.ru/eng/umn9429
  • https://doi.org/10.4213/rm9429
  • http://mi.mathnet.ru/eng/umn/v66/i4/p103

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

    This publication is cited in the following articles:
    1. M. I. Zelikin, “An analogue of Pontryagin's maximum principle in problems of minimization of multiple integrals”, Izv. Math., 81:5 (2017), 973–984  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. Osipov Yu.S., Zelikin M.I., “Fields of Smooth Compact Minimal Surfaces”, Russ. J. Math. Phys., 26:2 (2019), 174–179  crossref  isi
    3. M. I. Zelikin, Yu. S. Osipov, “Minimalnye podmnogoobraziya sfer i konusov”, Tr. IMM UrO RAN, 25, no. 3, 2019, 100–107  mathnet  crossref  elib
  • Успехи математических наук Russian Mathematical Surveys
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