Literature Cited
Yu. D. Burago, “Mutual restrictions on curvature and area for surfaces lying in the compact part of space,” Dokl. Akad. Nauk SSSR,179, No. 5, 1027–1028 (1968).
A. D. Aleksandrov, “Curve theory on the basis of broken-line approximation,” Uspekhi Matem. Nauk,2, No. 3, 182–184 (1947).
Yu. D. Burago and V. A. Zalgaller, “Realization of evolutes in the form of polyhedrons,” Vestnik Leningr. Goz. Yn-ta, No. 7, No. 2, 66–80 (1960).
L. A. Santalo, Introduction to Integral Geometry [Russian translation], IL, Moscow (1956).
A. D. Aleksandrov and V. A. Zalgaller, “Two-dimensional manifolds of restricted curvature.” Trudy Matem. In-ta Akad. Nauk SSSR,63 (1962).
Yu. D. Burago and V. A. Zalgaller, “Isoperimetric problem for restriction on the width of a region on a surface,” Trudy Matem. In-ta Akad. Nauk SSSR,76, 81–87 (1965).
T. Bonnesen, Les Problemes des Isoperimetres des Isepiphanes, Gauthier-Villars, Paris (1929).
V. K. Ionin, “Isoperimetric and other inequalities for manifolds of restricted curvature,” Sib. Matem. Zh.,X, No. 2, 329–342 (1969).
Yu. D. Burago and M. B. Stratilova, “Circles on surfaces,” Trudy Matem. In-ta Akad. Nauk SSSR,76, 88–114 (1965).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 10, No. 4, pp. 833–859, July–August, 1969.
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Burago, Y.D. Mutual restrictions of curvature and area of a surface in a sphere of fixed diameter. Sib Math J 10, 611–630 (1969). https://doi.org/10.1007/BF00973869
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DOI: https://doi.org/10.1007/BF00973869