Abstract
We prove the next result. If two isometric regular surfaces with regular boundaries, of an arbitrary finite genus, and positive Gaussian curvature in the three-dimensional Euclidean space, consist of two congruent arcs corresponding under the isometry (lying on the boundaries of these surfaces or inside these surfaces) then these surfaces are congruent.
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Translated from Sibirskii Matematicheskii Zhurnal, vol. 60, no. 1, pp. 109–117, January–February, 2019; DOI: 10.17377/smzh.2019.60.109.
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Klimentov, S.B. Unique Determination of Locally Convex Surfaces with Boundary and Positive Curvature of Genus p ≥ 0. Sib Math J 60, 82–88 (2019). https://doi.org/10.1134/S0037446619010099
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DOI: https://doi.org/10.1134/S0037446619010099