S. B. Klimentov, “Unique determination of locally convex surfaces with boundary and positive curvature of genus <nobr>$p\geqslant 0$</nobr>”, Sibirsk. Mat. Zh., 2019, Volume 60, Number 1,Pages <nobr>109

This article is cited in 3 papers

Unique determination of locally convex surfaces with boundary and positive curvature of genus $p\geqslant 0$

S. B. Klimentov^ab

^a Southern Federal University, Rostov-on-Don, Russia
^b Southern Mathematical Institute, Vladikavkaz, Russia

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.

UDC: 514.752.435

MSC: 35R30

Received: 19.04.2018
Revised: 08.10.2018
Accepted: 17.10.2018

DOI: 10.33048/smzh.2019.60.109