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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
Article
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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.

Keywords

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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