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Izvestiya: Mathematics, 2006, Volume 70, Issue 4, Pages 717–730
DOI: https://doi.org/10.1070/IM2006v070n04ABEH002325 (Mi im587) 		 
This article is cited in 12 scientific papers (total in 12 papers)

On some properties of stable and unstable surfaces with prescribed mean curvature

V. A. Klyachin

Volgograd State University
English version PDF (293 kB) Citations (12)
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DOI: https://doi.org/10.1070/IM2006v070n04ABEH002325
Abstract: We investigate the properties of stable (and unstable) hypersurfaces with prescribed mean curvature in Euclidean space and establish some necessary and sufficient tests for stability stated in terms of the external geometric structure of the surface. We prove an analogue of a well-known theorem of A. D. Aleksandrov that generalizes the variational property of the sphere and find an exact estimate for the extent of a stable tubular surface of constant mean curvature. Our method is based on an analysis of the first and second variations of area-type functionals for the surfaces under consideration.
Received: 23.09.2005
Revised: 13.03.2006
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2006, Volume 70, Issue 4, Pages 77–90
DOI: https://doi.org/10.4213/im587
Bibliographic databases:
UDC: 517.957+514.752
MSC: 49Q05, 49Q10, 53A10, 53C42, 76B45, 76D45
Language: English
Original paper language: Russian
Citation: V. A. Klyachin, “On some properties of stable and unstable surfaces with prescribed mean curvature”, Izv. RAN. Ser. Mat., 70:4 (2006), 77–90; Izv. Math., 70:4 (2006), 717–730
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v70/i4/p77
    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:531
    Russian version PDF:227
    English version PDF:16
    References:92
    First page:3
     
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