Integrable structure of the dirichlet boundary problem in multiply-connected domains

Communications in Mathematical Physics

Volumn 259, Issue 1, 2005, Pages 1-44

  Krichever, I ^a,b,c   Marshakov, A ^c,d,e   Zabrodin, A ^c,f  

^a Columbia University ^*  (United States)

^b LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

^c INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

^d MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

^e LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

^f EMANUEL INSTITUTE OF BIOCHEMICAL PHYSICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23944480888     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-005-1387-5     Document Type: Article

References (33)

1. Hurwitz, A., Courant, R.: Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen. Herausgegeben und ergänzt durch einen Abschnitt über geometrische Funktionentheorie. Berlin-Heidelberg-New York: Springer-Verlag, 1964
2. (Russian translation, adapted by M.A. Evgrafov: Theory of functions, Moscow: Nauka, 1968)
3. Marshakov, A., Wiegmann, P., Zabrodin, A.: Commun. Math. Phys. 227, 131 (2002)
4. Krichever, I.M.: Funct. Anal. Appl. 22, 200-213 (1989)
5. Krichever, I.M.: Commun. Pure. Appl. Math. 47, 437 (1994)
6. Mineev-Weinstein, M., Wiegmann, P.B., Zabrodin, A.: Phys. Rev. Lett. 84, 5106 (2000)
7. Wiegmann, P.B., Zabrodin, A.: Commun. Math. Phys. 213, 523 (2000)
8. Boyarsky, A., Marshakov, A., Ruchayskiy, O., Wiegmann, P., Zabrodin, A.: Phys. Lett. B515, 483-492 (2001)
9. Krichever, I., Novikov, S.: Funct. Anal. Appl. 21, No 2, 46-63 (1987)
10. Fay, J.D.: "Theta Functions on Riemann Surfaces". Lect. Notes in Mathematics 352, Berlin-Heidelberg-New York: Springer-Verlag, 1973
11. Hadamard, J.: Mém. présentés par divers savants à l'Acad. sci., 33, (1908)
12. Davis, P.J.: The Schwarz function and its applications. The Carus Mathematical Monographs, No. 17, Buffalo, N.Y.: The Math. Association of America, 1974
13. Krichever, I.: 2000, unpublished
14. Takhtajan, L.: Lett. Math. Phys. 56, 181-228 (2001)
15. Kostov, I.K., Krichever, I.M., Mineev-Weinstein, M., Wiegmann, P.B., Zabrodin, A.: τ-function for analytic curves. In: Random matrices and their applications, MSRI publications, 40, Cambridge: Cambridge Academic Press, 2001
16. Hille, E.: Analytic function theory. V.II, Oxford: Ginn and Company, 1962
17. Gibbons, J., Kodama,Y: Proceedings of NATO ASI "Singular Limits of Dispersive Waves", ed. N. Ercolani, London - New York: Plenum, 1994;
18. Carroll, R., Kodama, Y.: J. Phys. A: Math. Gen. A28, 6373 (1995)
19. Takasaki, K., Takebe, T.: Rev. Math. Phys. 7, 743-808 (1995)
20. Schiffer, M., Spencer, D.C.: Functionals of finite Riemann surfaces. Princeton, NJ: Princeton University Press, 1954
21. Gustafsson, B.: Acta Applicandae Mathematicae 1, 209-240 (1983)
22. Aharonov, D., Shapiro, H.: J. Anal. Math. 30, 39-73 (1976);
23. Shapiro, H.: The Schwarz function and its generalization to higher dimensions. University of Arkansas Lecture Notes in the Mathematical Sciences, Volume 9, W.H. Summers, Series Editor, New York: A Wiley-Interscience Publication, John Wiley and Sons, 1992
24. Etingof, P., Varchenko, A.: Why does the boundary of a round drop becomes a curve of order four? University Lecture Series. 3, Providence, RI: American Mathematical Society, 1992
25. Kazakov, V., Marshakov, A.: J. Phys. A: Math. Gen. 36, 3107-3136 (2003)
26. De Wit, B., Marshakov, A.: Theor. Math. Phys. 129, 1504 (2001)
27. [Teor. Mat. Fiz. 129, 230 (2001)]
28. Gakhov, F.: The boundary value problems. Moscow: Nauka, 1977 (in Russian)
29. Eynard, B.: Large N expansion of the 2-matrix model, multicut case. http://arxiv:org/list/math-ph/0307052, 2003
30. Bertola, M.: Free energy of the two-matrix model/dToda tau-function. Nucl. Phys. B669, 435-461 (2003)
31. Marshakov, A., Mironov, A., Morozov, A.: Phys. Lett. B389, 43-52 (1996);
32. Braden, H., Marshakov, A.: Phys. Lett. B541, 376-383 (2002)
33. Gorsky, A., Marshakov, A., Mironov, A., Morozov, A.: Nucl. Phys. B527, 690-716 (1998)