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Sib. Èlektron. Mat. Izv., 2007, Volume 4, Pages 113–132 (Mi semr148)  

This article is cited in 4 scientific papers (total in 4 papers)

Research papers

On the stability of extremal surfaces for a certain area type functional

V. A. Klyachin, N. M. Medvedeva

Volgograd State University

Abstract: In this paper we study the some questions about stability of the surfaces, which are the extremals of the area type functional. Stability, means, is called positively or negatively determined of second variation of functional for all any sufficiently small deformations of surface. In the work we obtain of the formulas first and second variation of functional, the capacity feature of instability, the conditions of stability and instability in the terms of the structure of surface image under Gaussian map. We consider some examples by application our results for research of stability of rotation surfaces.

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Document Type: Article
UDC: 514.772.2, 517.97
MSC: 53A40
Received March 6, 2006, published April 9, 2007

Citation: V. A. Klyachin, N. M. Medvedeva, “On the stability of extremal surfaces for a certain area type functional”, Sib. Èlektron. Mat. Izv., 4 (2007), 113–132

Citation in format AMSBIB
\Bibitem{KlyMed07}
\by V.~A.~Klyachin, N.~M.~Medvedeva
\paper On the stability of extremal surfaces for a~certain area type functional
\jour Sib. \`Elektron. Mat. Izv.
\yr 2007
\vol 4
\pages 113--132
\mathnet{http://mi.mathnet.ru/semr148}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2465418}
\zmath{https://zbmath.org/?q=an:1132.53302}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. M. Medvedeva, “Issledovanie ustoichivosti ekstremalnykh poverkhnostei vrascheniya”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 7:2 (2007), 25–32  mathnet  elib
    2. N. M. Poluboyarova, “Stability of $n$-dimensional extremal surfaces of revolution”, Russian Math. (Iz. VUZ), 55:2 (2011), 93–95  mathnet  crossref  mathscinet
    3. N. M. Poluboyarova, “Uravneniya ekstremalei funktsionala potentsialnoi energii”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 5(36), 60–72  mathnet  crossref
    4. N. M. Poluboyarova, “On instability of extremals of potential energy functional”, Ufa Math. J., 10:3 (2018), 77–85  mathnet  crossref  isi
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