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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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##### References:
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