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Izv. RAN. Ser. Mat., 1994, Volume 58, Issue 3, Pages 196–210 (Mi izv796)  

This article is cited in 3 scientific papers (total in 3 papers)

Conditions for finite existence time of maximal tubes and bands in Lorentzian warped products

V. A. Klyachin, V. M. Miklyukov

Volgograd State University

Abstract: Let $H$ be an $n$-dimensional Riemannian manifold, $\delta>0$ a smooth function on $H$, and $\widehat R$ the interval $(-\infty, +\infty)$ furnished with a negative definite metric $(-dt^2)$. Let $H\times_\delta\widehat R$ be the corresponding Lorentzian warped product [1, § 2.6]. We investigate the spacelike tubes and bands $\mathscr M$ with zero mean curvature in $\Omega\subset H$. It is shown that if $\mathscr M$ projects one-to-one onto some domain $\Omega\subset H$ of $\delta$-hyperbolic type, then $\mathscr M$ has a finite existence time. Examples are considered of maximal tubes and bands in Schwarzschild and de Sitter spaces. Geometric criteria are obtained for $\Omega$ to be of $\delta$-hyperbolic type.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1995, 44:3, 629–643

Bibliographic databases:

UDC: 517.97
MSC: Primary 53C40, 53C50; Secondary 83E30
Received: 26.06.1992

Citation: V. A. Klyachin, V. M. Miklyukov, “Conditions for finite existence time of maximal tubes and bands in Lorentzian warped products”, Izv. RAN. Ser. Mat., 58:3 (1994), 196–210; Russian Acad. Sci. Izv. Math., 44:3 (1995), 629–643

Citation in format AMSBIB
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\by V.~A.~Klyachin, V.~M.~Miklyukov
\paper Conditions for finite existence time of maximal tubes and bands in Lorentzian warped products
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\vol 58
\issue 3
\pages 196--210
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\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1995IzMat..44..629K}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1995
\vol 44
\issue 3
\pages 629--643
\crossref{https://doi.org/10.1070/IM1995v044n03ABEH001618}
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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. V. M. Miklyukov, “Some criteria for parabolicity and hyperbolicity of the boundary sets of surfaces”, Izv. Math., 60:4 (1996), 763–809  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. A. Klyachin, V. M. Miklyukov, “Criteria of instability of surfaces of zero mean curvature in warped Lorentz products”, Sb. Math., 187:11 (1996), 1643–1663  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Poluboyarova N.M., “Nekotorye otsenki \it{g}-emkosti ekstremalnykh poverkhnostei i sledstviya iz nikh1”, Vestnik volgogradskogo gosudarstvennogo universiteta. seriya 1: matematika. fizika, 2011, no. 2, 63–74  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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