Geodesic
Spectral Curves for Cauchy–Riemann Operators on Punctured Elliptic Curves
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 4, pp. 86-90 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We show that one can define a spectral curve for the Cauchy–Riemann operator on a punctured elliptic curve under appropriate boundary conditions. The algebraic curves thus obtained arise, for example, as irreducible components of the spectral curves of minimal tori with planar ends in $\mathbb{R}^3$. It turns out that these curves coincide with the spectral curves of certain elliptic KP solitons studied by Krichever.
Keywords: Cauchy–Riemann operator, spectral curve
Mots-clés : elliptic soliton. 
@article{FAA_2013_47_4_a7,
     author = {{\CYRS}. Bohle and I. A. Taimanov},
     title = {Spectral {Curves} for {Cauchy{\textendash}Riemann} {Operators} on {Punctured} {Elliptic} {Curves}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {86--90},
     year = {2013},
     volume = {47},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2013_47_4_a7/}
}
TY  - JOUR
AU  - С. Bohle
AU  - I. A. Taimanov
TI  - Spectral Curves for Cauchy–Riemann Operators on Punctured Elliptic Curves
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2013
SP  - 86
EP  - 90
VL  - 47
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/FAA_2013_47_4_a7/
LA  - ru
ID  - FAA_2013_47_4_a7
ER  - 
%0 Journal Article
%A С. Bohle
%A I. A. Taimanov
%T Spectral Curves for Cauchy–Riemann Operators on Punctured Elliptic Curves
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2013
%P 86-90
%V 47
%N 4
%U http://geodesic.mathdoc.fr/item/FAA_2013_47_4_a7/
%G ru
%F FAA_2013_47_4_a7
С. Bohle; I. A. Taimanov. Spectral Curves for Cauchy–Riemann Operators on Punctured Elliptic Curves. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 4, pp. 86-90. http://geodesic.mathdoc.fr/item/FAA_2013_47_4_a7/

[1] S. P. Novikov, Funkts. analiz i ego pril., 8:3 (1974), 54–66 | MR | Zbl

[2] B. A. Dubrovin, I. M. Krichever, S. P. Novikov, Dokl. AN SSSR, 229:1 (1976), 15–18 | MR | Zbl

[3] I. M. Krichever, Funkts. analiz i ego pril., 14:4 (1980), 45–54 | MR | Zbl

[4] I. A. Taimanov, Funkts. analiz i ego pril., 32:4 (1998), 49–62 | DOI | MR | Zbl

[5] I. M. Krichever, UMN, 44:2(266) (1989), 121–184 | MR | Zbl

[6] B. G. Konopelchenko, Stud. Appl. Math., 96:1 (1996), 9–52 | DOI | MR

[7] I. A. Taimanov, Solitons, Geometry, and Topology: on the Crossroad, Amer. Math. Soc. Transl., Ser. 2, 179, 1997, 133–151 | MR | Zbl

[8] R. L. Bryant, J. Differential Geom., 20:1 (1984), 23–53 | DOI | MR | Zbl

[9] C. Bohle, J. Differential Geom., 86:1 (2010), 71–131 | DOI | MR | Zbl

[10] C. Bohle, I. A. Taimanov, “Euclidean minimal tori with planar ends and elliptic solitons” (to appear)