Siberian Mathematical Journal

, Volume 60, Issue 1, pp 82–88 | Cite as

Unique Determination of Locally Convex Surfaces with Boundary and Positive Curvature of Genus p ≥ 0

  • S. B. KlimentovEmail author


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.


bending of a surface unique determination 


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Southern Federal UniversityRostov-on-DonRussia
  2. 2.Southern Mathematical InstituteVladikavkazRussia

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