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Book Review
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Book Information
Author(s):
J. Feldman, H. K\"norrer and E. Trubowitz
Title:
Riemann surfaces of infinite genus
Additional book information:
CRM Monograph series, vol. 20, Amer. Math. Soc.,
Providence, RI,
2003,
303,
$79.00,
0-8218-3357-X
References:
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- [1961]
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- [1958]
- ANDREOTTI, A.: On a theorem of Torelli. Amer. J. Math. 80 (1958) 801-828. MR 0102518 (21:1309)
- [1984]
- ARBARELLO, E., and DE CONCINI, C.: On a set of equations characterizing Riemann matrices. Ann. Math. 120 (1984) 119-140. MR 0750718 (86a:14025)
- [1897]
- BAKER, H.F.: Abelian Functions. Cambridge U. Press, Cambridge, 1897; reissued 1995. MR 1386644 (97b:14038)
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- -: An Introduction to the Theory of Multiply Periodic Functions. Cambridge U. Press, Cambridge, 1967.
- [1976]
- DYSON, F.: Fredholm determinants and inverse scattering problems. Comm. Math. Phys. 47 (1976) 171-183. MR 0406201 (53:9993)
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- FADDEEV, L., and ZAKHAROV, V.: Korteweg-de Vries equation: a completely integrable Hamiltonian system. Funkt. Anal. Pril. 5 (1971) 280-287. MR 0303132 (46:2270)
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- GARDINER, R., GREENE, J., KRUSKAL, M., and MIURA, R.: Method for solving the Korteweg-de Vries equation. Phys. Rev. Letters 19 (1967) 1095-1097.
- [1952]
- HEINS, M.: Riemann surfaces of infinite genus. Ann. Math. (2) 55 (1952) 296-317. MR 0045834 (13:643d)
- [1975]
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- KOVALEVSKAYA, S.: Sur le probleme de la rotation d'un corps autour d'un point fixe. Acta Math. 12 (1889) 177-232. Norehnye Raboty, Acad. Sci. USSR, 1948. MR 1916790
- [1968]
- LAX, P.: Integrals of nonlinear equations of evolution and solitary waves. CPAM 21 (1968) 467-490.MR 0235310 (38:3620)
- [1975]
- -: Periodic solutions of the Korteweg-de Vries equation. CPAM 28 (1975) 141-189. MR 0369963 (51:6192)
- [1990]
- MCKEAN, H.P., and ERCOLANI, N.: Geometry of KdV (4): Abel sums, Jacobi variety, and theta function in the scattering case. Invent. Math. 99 (1990) 482-544. MR 1032878 (91f:58038)
- [1975]
- MCKEAN, H.P., and VAN MOERBEKE, P.: The spectrum of Hill's equation. Invent. Math. 30 (1975) 217-274. MR 0397076 (53:936)
- [1976]
- MCKEAN, H.P., and TRUBOWITZ, E.: Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points. CPAM 29 (1976) 143-226. MR 0427731 (55:761)
- [1978]
- -: Hill's surfaces and their theta functions. BAMS 84 (1978) 1042-1085. MR 0508448 (80b:30039)
- [2000]
- MERKL, F.: A Riemann-Roch Theorem for infinite genus Riemann surfaces. Invent. Math. 139 (2000) 391-437. MR 1738447 (2001e:32030)
- [1943]
- MYRBERG, P.J.: Über tranzendente hyperellipische Integrale erster Gattung. Ann. Acad. Sci. Fenn. 14 (1943) 1-32. MR 0015497 (7:428a)
- [1945]
- -: Über analytische Funktionen auf tranzendenten zweiblättrigen Riemannschen Flächen mit realen verzweigungspunkten. Acta Math. 76 (1945) 185-244. MR 0012675 (7:57d)
- [1996]
- -: Über analytische Funktionen auf tranzendenten Riemannschen Flächen. 10th. Cong. Math. Scand., Copenhagen, 1947, pp. 77-96. MR 0020146 (8:509b)
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Additional Information:
Reviewer(s):
Henry
P.
McKean
Affiliation:
Courant Institute of Mathematical Sciences
Email:
mckean@cims.nyu.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
42
(2005),
79-87.
MSC
(2000):
Primary 30-XX, 58-XX
DOI:
10.1090/S0273-0979-04-01030-4
PII:
S 0273-0979(04)01030-4
Posted:
September 23, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
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