Geodesic
Isothermic coordinates on irregular sewing surfaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 658-676.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: isothermic coordinates, sewing surfaces, sewing homeomorphisms. 
@article{SEMR_2018_15_a44,
     author = {A. N. Kondrashov},
     title = {Isothermic coordinates on irregular sewing surfaces},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {658--676},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a44/}
}
TY  - JOUR
AU  - A. N. Kondrashov
TI  - Isothermic coordinates on irregular sewing surfaces
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 658
EP  - 676
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a44/
LA  - ru
ID  - SEMR_2018_15_a44
ER  - 
%0 Journal Article
%A A. N. Kondrashov
%T Isothermic coordinates on irregular sewing surfaces
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 658-676
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a44/
%G ru
%F SEMR_2018_15_a44
A. N. Kondrashov. Isothermic coordinates on irregular sewing surfaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 658-676. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a44/

[1] Sb. Math., 195:1–2 (2004), 65–83 | DOI | DOI | MR | Zbl | Zbl

[2] V.M. Miklyukov, Conformal Maps of Nonsmooth Surfaces and Their Applications, Exlibris Corporation, Philadelphia, 2008

[3] V.M. Miklyukov, Function Weighted Sobolev Classes, Anisotropic Metric and Degenerate Quasi-Conformal Mappings, VolSU, Volgograd, 2010

[4] C. Carathéodory, Conformal representation, Cambridge Univ. Press, London, 1932 | Zbl

[5] Geometry IV, Encyclopaedia Math. Sci., 70, Springer-Verlag, Berlin, 1993 | DOI | MR | Zbl

[6] T. Toro, “Surfaces with generalized second fundamental form in $L^2$ are Lipschitz manifolds”, J. Differential Geom., 39:1 (1994), 65-–101 | DOI | MR | Zbl

[7] S. Müller and V. Sverák, “On surfaces of finite total curvature”, J. Differential Geom., 42:2 (1995), 229–-258 | DOI | MR | Zbl

[8] I.M. Grudskiǐ, “Construction of inner coordinates on composite Riemann surfaces”, Differential, integral equations, and complex analysis, Kalmykia University, Élista, 1986, 30–-45 (Russian) | MR

[9] Soviet Math. Dokl., 40 (1990) | MR

[10] L.V. Ahlfors, Lectures on quasiconformal mappings, Manuscript prepared with the assistance of Clifford J. Earle, Jr., Van Nostrand Mathematical Studies, 10, D. Van Nostrand Co., Inc., Toronto, Ont.–New York–London, 1966 | MR | Zbl

[11] L.I. Volkovyskiǐ, “Investigation of the type problem for a simply connected Riemann surface”, Trudy Mat. Inst. Steklov, 34, 1950 (Russian) | MR

[12] Siberian Math. J., 20 (1979), 298–301 | DOI | MR | Zbl | Zbl

[13] V.G. Maz'ya, Sobolev Spaces. With Applications to Elliptic Partial Differential Equations, Grundlehren der Mathematischen Wissenschaften, 342, 2nd revised and augmented ed., Springer Verlag, Berlin–Heidelberg–New York, 2011 | DOI | MR | Zbl

[14] V.G. Maz’ya, S.V. Poborchii, Embedding theorems and continuation of functions in non-Lipschitz domains, St. Petersburg State Univ., St. Petersburg, 2006

[15] A.N. Kondrashov, “On the theory of degenerate alternating Beltrami equations”, Sibirsk. Mat. Zh., 53:6 (2012), 1321–1337 | MR | Zbl

[16] A.N. Kondrashov, “On the theory of alternating beltrami equation with many folds”, Science Journal of VolSU. Mathematics. Physics, 19:2 (2013), 26–35

[17] A.N. Kondrashov, “Beltrami equations with degenerate on arcs”, Science Journal of VolSU. Mathematics. Physics, 24:5 (2014), 24–39

[18] A.N. Kondrashov, “Alternating Beltrami equation and conformal multifolds”, Science Journal of VolSU. Mathematics. Physics, 30:5 (2015), 6–24