The One-Dimensional Riemann Problem on an Elliptic Curve
Matematičeskie zametki, Tome 101 (2017) no. 1, pp. 91-100.

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

A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and the explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic.
Keywords: Riemann problem, elliptic curve, logarithmic connection.
@article{MZM_2017_101_1_a7,
     author = {A. A. Matveeva and V. A. Poberezhnyi},
     title = {The {One-Dimensional} {Riemann} {Problem} on an {Elliptic} {Curve}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {91--100},
     publisher = {mathdoc},
     volume = {101},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_1_a7/}
}
TY  - JOUR
AU  - A. A. Matveeva
AU  - V. A. Poberezhnyi
TI  - The One-Dimensional Riemann Problem on an Elliptic Curve
JO  - Matematičeskie zametki
PY  - 2017
SP  - 91
EP  - 100
VL  - 101
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2017_101_1_a7/
LA  - ru
ID  - MZM_2017_101_1_a7
ER  - 
%0 Journal Article
%A A. A. Matveeva
%A V. A. Poberezhnyi
%T The One-Dimensional Riemann Problem on an Elliptic Curve
%J Matematičeskie zametki
%D 2017
%P 91-100
%V 101
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2017_101_1_a7/
%G ru
%F MZM_2017_101_1_a7
A. A. Matveeva; V. A. Poberezhnyi. The One-Dimensional Riemann Problem on an Elliptic Curve. Matematičeskie zametki, Tome 101 (2017) no. 1, pp. 91-100. http://geodesic.mathdoc.fr/item/MZM_2017_101_1_a7/

[1] A. A. Bolibrukh, “21-ya problema Gilberta dlya lineinykh fuksovykh sistem”, Tr. MIAN, 206, Nauka, M., 1994, 3–158 | MR | Zbl

[2] A. A. Bolibrukh, Obratnye zadachi monodromii v analiticheskoi teorii differentsialnykh uravnenii, MTsNMO, M., 2009

[3] R. R. Gontsov, V. A. Poberezhnyi, “Razlichnye varianty problemy Rimana–Gilberta dlya lineinykh differentsialnykh uravnenii”, UMN, 63:4 (382) (2008), 3–42 | DOI | MR | Zbl

[4] V. V. Prasolov, Yu. P. Solovev, Ellipticheskie funktsii i algebraicheskie uravneniya, Faktorial, M., 1997