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Mat. Sb., 1996, Volume 187, Number 6, Pages 119–130 (Mi msb140)  

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

On Efimov surfaces that are rigid 'in the small'

Z. D. Usmanov

Institute of Mathematics, Academy of Sciences of Republic of Tajikistan

Abstract: We consider rigid (in the class of analytic infinitesimal bendings) analytic surfaces with an isolated point of flattening and positive Gaussian curvature around this point. It is proved that such surfaces are rigid 'in the small' in the class $C^\infty$. The proof is based on the study of the asymptotic behaviour of the field of infinitesimal bending in a neighbourhood of the point of flattening and subsequent application of the techniques of the theory of generalized Cauchy–Riemann systems with a singularity in the coefficients.

DOI: https://doi.org/10.4213/sm140

Full text: PDF file (259 kB)
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English version:
Sbornik: Mathematics, 1996, 187:6, 903–915

Bibliographic databases:

UDC: 514.752.43
MSC: 53A05, 53C45
Received: 25.03.1994

Citation: Z. D. Usmanov, “On Efimov surfaces that are rigid 'in the small'”, Mat. Sb., 187:6 (1996), 119–130; Sb. Math., 187:6 (1996), 903–915

Citation in format AMSBIB
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\paper On Efimov surfaces that are rigid 'in the~small'
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\yr 1996
\vol 187
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\pages 119--130
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\transl
\jour Sb. Math.
\yr 1996
\vol 187
\issue 6
\pages 903--915
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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. Meziani, A, “Infinitesimal bendings of homogeneous surfaces with nonnegative curvature”, Communications in Analysis and Geometry, 11:4 (2003), 697  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Meziani A., “Planar complex vector fields and infinitesimal bendings of surfaces with nonnegative curvature”, Recent Progress on Some Problems in Several Complex Variables and Partial Differential Equations, Contemporary Mathematics Series, 400, 2006, 189–201  crossref  mathscinet  zmath  isi
    3. Meziani, A, “Infinitesimal bendings of high orders for homogeneous surfaces with positive curvature and a flat point”, Journal of Differential Equations, 239:1 (2007), 16  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. Meziani A., “Nonrigidity of a Class of Two Dimensional Surfaces with Positive Curvature and Planar Points”, Proc. Amer. Math. Soc., 141:6 (2013), 2137–2143  crossref  mathscinet  zmath  isi  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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