MG-deformations of a surface of positive Gaussian curvature under assignment of variation of any tensor along an edge

We investigate the infinitesimal MG-deformations of a simply connected surface with positive Gaussian curvature. We choose any symmetric tensor on the surface, variation of the first and the second invariant of this tensor equals given function along a boundary. The study of these boundary-value pro...

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Bibliographic Details
Published in:Russian mathematics 2017-12, Vol.61 (12), p.13-18
Main Author: Zhukov, D. A.
Format: Article
Language:English
Subjects:
Boundary value problems
Curvature
Deformation
Existence theorems
Mathematical analysis
Mathematics
Mathematics and Statistics
Uniqueness theorems
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Summary:We investigate the infinitesimal MG-deformations of a simply connected surface with positive Gaussian curvature. We choose any symmetric tensor on the surface, variation of the first and the second invariant of this tensor equals given function along a boundary. The study of these boundary-value problems is reduced to the investigation of a solvability of Riemann–Hilbert boundary-value problem and to calculation of its index. As a result we get theorems of existence and uniqueness for the infinitesimal MG-deformation.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X17120027