Abstract:
In this paper we investigate the stability of surfaces of zero mean curvature in Lorentz manifolds. In the case when the enveloping manifold is a warped Lorentz product and under certain assumptions about the warping function, it is proved that every stable minimal tube or strip is a totally geodesic manifold.
Citation:
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
\Bibitem{KlyMik96}
\by V.~A.~Klyachin, V.~M.~Miklyukov
\paper Criteria of instability of surfaces of zero mean curvature in warped Lorentz products
\jour Sb. Math.
\yr 1996
\vol 187
\issue 11
\pages 1643--1663
\mathnet{http://mi.mathnet.ru/eng/sm172}
\crossref{https://doi.org/10.1070/SM1996v187n11ABEH000172}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1438984}
\zmath{https://zbmath.org/?q=an:0879.53041}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1996WQ48500003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0030299670}
Linking options:
https://www.mathnet.ru/eng/sm172
https://doi.org/10.1070/SM1996v187n11ABEH000172
https://www.mathnet.ru/eng/sm/v187/i11/p67
This publication is cited in the following 12 articles:
N. M. Poluboyarova, “Relations between length and instability of tubular extremal surfaces”, Ufa Math. J., 13:1 (2021), 77–84
A. A. Klyachin, V. A. Klyachin, “Research in the field of geometric analysis at Volgograd state university”, Mathematical Physics and Computer Simulation, 23:2 (2020), 5–21
N. M. Poluboyarova, “On instability of extremals of potential energy functional”, Ufa Math. J., 10:3 (2018), 77–85
Bulawa A., “Maximal Hypersurfaces in Spacetimes With a Nonvanishing Spacelike Killing Field”, Ann. Henri Poincare, 18:11 (2017), 3633–3649
N. M. Poluboyarova, “Uravneniya ekstremalei funktsionala potentsialnoi energii”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 5(36), 60–72
N. M. Poluboyarova, “Stability of n-dimensional extremal surfaces of revolution”, Russian Math. (Iz. VUZ), 55:2 (2011), 93–95
N. M. Medvedeva, “Issledovanie ustoichivosti ekstremalnykh poverkhnostei vrascheniya”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 7:2 (2007), 25–32
V. A. Klyachin, N. M. Medvedeva, “Ob ustoichivosti ekstremalnykh poverkhnostei nekotorykh funktsionalov tipa ploschadi”, Sib. elektron. matem. izv., 4 (2007), 113–132
Asperti, AC, “Bjorling problem for spacelike, zero mean curvature surfaces in L-4”, Journal of Geometry and Physics, 56:2 (2006), 196
Klyachin, VA, “The stability and instability of surfaces with prescribed mean curvature”, Doklady Mathematics, 72:1 (2005), 603
Citation in format AMSBIB
Contact us: