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Literature cited
B. V. Dekster, “An isoperimetric type inequality for a domain in a Riemannian space,” Mat. Sb.,90, No. 2, 257–274 (1973).
Yu. D. Burago and V. A. Zalgaller, “Dependence of the volume of a domain in a Riemannain manifold on the curvature of the space and the boundary,” Preprint Leningrad Branch of the Mathematics Institute, P-4-78, Nauka, Leningrad (1978).
V. Ionin, “On isoperimetric and certain other inequalities for manifolds of bounded curvature,” Sib. Mat. Zh.,10, No. 2, 329–342 (1969).
D. Hoffman and J. Spruck, “Sobolev and isoperimetric inequalities for Riemannian submanifolds,” Commun. Pure Appl. Math.,27, No. 6, 715–727 (1974).
M. Buchner, “Simplicial structure of the real analytic cut locus,” Proc. Am. Math. Soc.,64, No. 1, 118–121 (1977).
R. L. Bishop and R. J. Crittenden, Geometry of Manifolds, Academic Press, New York-London (1964).
A. P. Mostovskoi, “On a generalization of convex sets in a Riemannian space,” in: Questions of Global Geometry [in Russian], 31st Hertzian Lectures, Leningrad. Pedagog. Inst. im Gertsena (1978), pp. 21–27.
R. Greene and H. Wu, “On the subharmonicity and plurisubharmonicity of geodesically convex functions,” Indiana Univ. Math. J.,22, 641–654 (1973).
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Translated from Matematicheskie Zametki, Vol. 28, No. 1, pp. 103–112, July, 1980.
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Burago, Y.D. Certain inequalities for mean curvature, area, and volume in a Riemannian manifold. Mathematical Notes of the Academy of Sciences of the USSR 28, 516–521 (1980). https://doi.org/10.1007/BF01159432
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DOI: https://doi.org/10.1007/BF01159432