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Sibirskii Matematicheskii Zhurnal, 2004, Volume 45, Number 1, Pages 25–61 (Mi smj1062)  
This article is cited in 28 scientific papers (total in 28 papers)

Irregular $C^{1,\beta}$-surfaces with an analytic metric

Yu. F. Borisov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (381 kB) Citations (28)
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Abstract: We prove that in the class $C^{1,\beta}$ with $\beta<1/13$ it is possible to continuously deform an analytic convex surface of positive Gaussian curvature (or a plane) so as to lose boundedness of the extrinsic curvature in the Pogorelov sense. We demonstrate how to replace the bound $\beta<1/13$ with $\beta<1/7$.
Keywords: continuous deformation, analytic surface, positive Gaussian curvature, local convexity.
Received: 04.08.2002
English version:
Siberian Mathematical Journal, 2004, Volume 45, Issue 1, Pages 19–52
DOI: https://doi.org/10.1023/B:SIMJ.0000013011.51242.23
Bibliographic databases:
UDC: 513.81
Language: Russian
Citation: Yu. F. Borisov, “Irregular $C^{1,\beta}$-surfaces with an analytic metric”, Sibirsk. Mat. Zh., 45:1 (2004), 25–61; Siberian Math. J., 45:1 (2004), 19–52
Citation in format AMSBIB
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\by Yu.~F.~Borisov
\paper Irregular $C^{1,\beta}$-surfaces with an analytic metric
\jour Sibirsk. Mat. Zh.
\yr 2004
\vol 45
\issue 1
\pages 25--61
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\zmath{https://zbmath.org/?q=an:1054.53081}
\transl
\jour Siberian Math. J.
\yr 2004
\vol 45
\issue 1
\pages 19--52
\crossref{https://doi.org/10.1023/B:SIMJ.0000013011.51242.23}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000189126800004}
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    • This publication is cited in the following 28 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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