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Mathematics of the USSR-Izvestiya, 1992, Volume 38, Issue 1, Pages 203–213
DOI: https://doi.org/10.1070/IM1992v038n01ABEH002194
(Mi im1033)
 

This article is cited in 10 scientific papers (total in 10 papers)

Maximal tubular hypersurfaces in Minkowski space

V. A. Klyachin, V. M. Miklyukov
References:
Abstract: Consider $C^2$-solutions of the equations for maximal surfaces in Minkowski space
$$ \sum_{i=1}^n \frac\partial{\partial x_i}\left(\frac{fx_i}{\sqrt{1-|\nabla f|^2}}\right)=0. $$

The hypersurface $t=f(x)$ is tubular if for every $\tau$ the level sets $E_\tau=\{x\colon f(x)=\tau\}$ are compact. The girth function of a tubular hypersurface is given by $\rho(\tau)=\max\limits_{x\in E_\tau}|x|$.
In this paper it is shown that the girth function of a maximal tubular surface satisfies the differential inequality $\rho(t)\rho ''(t)\geqslant(n-1)(\rho^{'2}(t)-1)$.
As a consequence of this assertion it is established that the union of the rays tangent to the hypersurface at an isolated singular point forms the light cone; a bound is obtained, in the neighborhood of an isolated singularity, to the spread of the maximal tube in the direction of the time axis in terms of its deviation from the light cone.
Received: 28.11.1989
Bibliographic databases:
UDC: 517.95
MSC: Primary 53D10; Secondary 53C50
Language: English
Original paper language: Russian
Citation: V. A. Klyachin, V. M. Miklyukov, “Maximal tubular hypersurfaces in Minkowski space”, Math. USSR-Izv., 38:1 (1992), 203–213
Citation in format AMSBIB
\Bibitem{KlyMik91}
\by V.~A.~Klyachin, V.~M.~Miklyukov
\paper Maximal tubular hypersurfaces in Minkowski space
\jour Math. USSR-Izv.
\yr 1992
\vol 38
\issue 1
\pages 203--213
\mathnet{http://mi.mathnet.ru//eng/im1033}
\crossref{https://doi.org/10.1070/IM1992v038n01ABEH002194}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1130035}
\zmath{https://zbmath.org/?q=an:0747.53048|0732.53049}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1992IzMat..38..203K}
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  • https://doi.org/10.1070/IM1992v038n01ABEH002194
  • https://www.mathnet.ru/eng/im/v55/i1/p206
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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