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Stability of \(n\)-dimensional extremal surfaces of revolution. (English. Russian original) Zbl 1228.53007
Russ. Math. 55, No. 2, 93-95 (2011); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2011, No. 2, 106-109 (2011).
Summary: We consider extremal surfaces of revolution of area-type functionals. For the latter, we calculate the first and second variations. We prove stability and instability criteria for \(n\)-dimensional surfaces of revolution based on their definition and in terms of special integrals.
MSC:
53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
49Q10 Optimization of shapes other than minimal surfaces
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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[1] A. A. Tuzhilin, ”Morse-Type Indices of Two-Dimensional Minimal Surfaces in R3 and H3,” Izv. Akad. Nauk SSSR, Ser.Matem. 55(2), 581–607 (1991). · Zbl 0746.49030
[2] V. A. Klyachin and V. M. Miklyukov, ”Criteria of Instability of Surfaces of Zero Mean Curvature in Warped Lorentz Products,” Matem. Sborn. 187(11), 67–88 (1996). · Zbl 0879.53041
[3] V. A. Klyachin and N. M. Medvedeva, ”On the Stability of Extremal Surfaces for a Certain Area Type Functional,” Sibirskie ElektronnyeMatematicheskie Izvestiya 4, 113–132 (2007). · Zbl 1132.53302
[4] A. D. Vedenyapin and V. M. Miklyukov, ”Extrinsic Dimensions of Tubular Minimal Hypersurfaces,” Matem. Sborn. 131, 240–250 (1986). · Zbl 0621.53006
[5] N. M. Medvedeva, ”Stability of Extremal Surfaces of Revolution,” Izvestiya Saratovskogo Universiteta. Ser. Matematika. Mekhanika. Informatika 7(2), 25–32 (2007).
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