Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1. Mathematica. Physica
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Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1. Mathematica. Physica, 2016, Issue 6(37), Pages 70–80
DOI: https://doi.org/10.15688/jvolsu1.2016.6.7
(Mi vvgum147)
 

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Isothermic coordinates on sewing surfaces

A. N. Kondrashov

Volgograd State University
Full-text PDF (408 kB) Citations (1)
References:
Abstract: In the paper we investigated of question about existence and uniqueness of isothermic coordinates on sewing surfaces in $\mathbb{R}^m$. The such surfaces is special case of irregular surfaces. We obtained the analog of the famous theorem of V.M. Miklukov (2004) for such surfaces.
The result of this paper.
Theorem 2. Let $\mathcal{X}_{12}$ be a pasting together of the pair of the surfaces $\mathcal{X}_i=(G_i,f_i)$, $(i=1,2)$ and $\Gamma_i=\partial G_i$ is quasistraight line. Let be a $\varphi_{12}:\Gamma_{1}\to\Gamma_{2}$ is sewing function.
Assume that $\varphi_{12}$ is quasimonotone function and that
$$P_i(x^{(i)})=\frac{E_i(x^{(i)})+G_i(x^{(i)})}{\sqrt{E_i(x^{(i)})G_i(x^{(i)} )-F_i^2(x^{(i)})}}, \ i=1,2,$$
is $W^{1,2}_{\mathrm{loc},\Gamma_i}$-majorized functions in $G_i$.
There is exist isothermic coordinates $\xi=(\xi_1,\xi_2) \in B(O,R)$, $R>1$ on $\mathcal{X}_{12}$. These coordinates are determined uniquely by choice of correspondence $a\longleftrightarrow O$, $b\longleftrightarrow \Xi$, where either the $a, b\in G_{i}\cup\Gamma_{i}(i=1,2)$ and $a\ne b$, or $a\in G_1$, $b\in G_2$ and $a\ne\varphi_{12}(b)$.
Keywords: isothermic coordinates, sewing surfaces, sewing functions, quasisymmetric function, $W^{1,2}_{\mathrm{loc},\Gamma}$-majorized functions, quasistraight line.
Document Type: Article
UDC: 514.752.44:514.772:517.548
BBC: 22.15
Language: Russian
Citation: A. N. Kondrashov, “Isothermic coordinates on sewing surfaces”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1. Mathematica. Physica, 2016, no. 6(37), 70–80
Citation in format AMSBIB
\Bibitem{Kon16}
\by A.~N.~Kondrashov
\paper Isothermic coordinates on sewing surfaces
\jour Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1. Mathematica. Physica
\yr 2016
\issue 6(37)
\pages 70--80
\mathnet{http://mi.mathnet.ru/vvgum147}
\crossref{https://doi.org/10.15688/jvolsu1.2016.6.7}
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