Geodesic
An analog of the Gauss--Aleksandrov theorem about the area of the spherical image of a nonconvex polyhedral angle without singularities
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 2, Tome 221 (2023), pp. 10-19.

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In this paper, we formulate the definitions of еру spherical image, the area of the spherical image, and the implementation curvature for a class of polyhedral angles without singularities. Also, we prove a theorem on the equality of the area of the spherical image and the implementation curvature of a polyhedral angle from a distinguished class.
Keywords: Gauss theorem, area of a spherical image, nonconvex polyhedron, implementation curvature. 
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     title = {An analog of the {Gauss--Aleksandrov} theorem about the area of the spherical image of a nonconvex polyhedral angle without singularities},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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L. A. Antipova. An analog of the Gauss--Aleksandrov theorem about the area of the spherical image of a nonconvex polyhedral angle without singularities. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 2, Tome 221 (2023), pp. 10-19. http://geodesic.mathdoc.fr/item/INTO_2023_221_a1/

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[2] Aleksandrov A. D., Verner A. L., Ryzhik V. I., Geometriya 11. Uchebnik dlya uglublennogo izucheniya, Prosveschenie, M., 2000

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