Abstract:
The objects investigated are simply connected pieces of surfaces of positive curvature with isolated flat points. Infinitesimal deformations under given boundary conditions are studied. The deformation situation depends essentially on the order of tangency of the surface with its tangent plane at the flat point, as well as on the index of the boundary condition.
The geometric results are based on the solution of the Riemann–Hilbert problem for generalized Cauchy–Riemann systems with singular coefficients.
Bibliography: 8 titles.
\Bibitem{Usm72}
\by Z.~D.~Usmanov
\paper On~a~problem concerning the deformation of a~surface with a~flat point
\jour Math. USSR-Sb.
\yr 1972
\vol 18
\issue 1
\pages 61--81
\mathnet{http://mi.mathnet.ru/eng/sm3217}
\crossref{https://doi.org/10.1070/SM1972v018n01ABEH001612}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=313980}
\zmath{https://zbmath.org/?q=an:0258.53006}
Linking options:
https://www.mathnet.ru/eng/sm3217
https://doi.org/10.1070/SM1972v018n01ABEH001612
https://www.mathnet.ru/eng/sm/v131/i1/p61
This publication is cited in the following 2 articles:
I. Ivanova-Karatopraklieva, I. Kh. Sabitov, “Surface deformation. I”, Journal of Mathematical Sciences (New York), 70:2 (1994), 1685
Z.D. Usmanov, “Generalized cauchy—riemann systems with a singular point”, Complex Variables, Theory and Application: An International Journal, 26:1-2 (1994), 41
Citation in format AMSBIB
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