American Mathematical Society

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

MathSciNet review: 1568059
Full text of review: PDF This review is available free of charge.
Book Information:

Author: Anthony J.~Tromba
Title: Teichm\"uller theory in Riemannian geometry
Additional book information: Birkhauser-Verlag, Basel, 1992, 222 pp., US$29.00. ISBN 3-7643-2735-9.

William Abikoff, The real analytic theory of Teichmüller space, Lecture Notes in Mathematics, vol. 820, Springer, Berlin, 1980. MR 590044

Lars V. Ahlfors, The complex analytic structure of the space of closed Riemann surfaces. , Analytic functions, Princeton Univ. Press, Princeton, N.J., 1960, pp. 45–66. MR 0124486

Lars V. Ahlfors, Some remarks on Teichmüller’s space of Riemann surfaces, Ann. of Math. (2) 74 (1961), 171–191. MR 204641, DOI 10.2307/1970309

Lars V. Ahlfors, Curvature properties of Teichmüller’s space, J. Analyse Math. 9 (1961/62), 161–176. MR 136730, DOI 10.1007/BF02795342

Lipman Bers, Correction to “Spaces of Riemann surfaces as bounded domains”, Bull. Amer. Math. Soc. 67 (1961), 465–466. MR 130972, DOI 10.1090/S0002-9904-1961-10637-X

Lipman Bers and Leon Ehrenpreis, Holomorphic convexity of Teichmüller spaces, Bull. Amer. Math. Soc. 70 (1964), 761–764. MR 168800, DOI 10.1090/S0002-9904-1964-11230-1

[FK]

R. Fricke and F. Klein, Vorlesungen über die theorie der automorphen funktionen, Teubner, Lepzig, 1926.

John Hubbard and Howard Masur, Quadratic differentials and foliations, Acta Math. 142 (1979), no. 3-4, 221–274. MR 523212, DOI 10.1007/BF02395062

Jürgen Jost, Two-dimensional geometric variational problems, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1991. A Wiley-Interscience Publication. MR 1100926

Linda Keen, On Fricke moduli, Advances in the Theory of Riemann Surfaces (Proc. Conf., Stony Brook, N.Y., 1969) Ann. of Math. Studies, No. 66, Princeton Univ. Press, Princeton, N.J., 1971, pp. 205–224. MR 0288252

Steven Kerckhoff, Howard Masur, and John Smillie, Ergodicity of billiard flows and quadratic differentials, Ann. of Math. (2) 124 (1986), no. 2, 293–311. MR 855297, DOI 10.2307/1971280

Yair N. Minsky, Harmonic maps, length, and energy in Teichmüller space, J. Differential Geom. 35 (1992), no. 1, 151–217. MR 1152229

Dennis Sullivan, Quasiconformal homeomorphisms and dynamics. I. Solution of the Fatou-Julia problem on wandering domains, Ann. of Math. (2) 122 (1985), no. 3, 401–418. MR 819553, DOI 10.2307/1971308

[T1]

O. Teichmüller, Extremale quasikonforme abbildungen und quadratisihe differentiale, Preuss. Akad. 22 (1939).

[T2]

-, Bestimmung der extremalen quasi konforme Abbildungen bei geschlossen orientierten Riemannschen Flächen, Preuss. Akad. 4 (1943).

Friedrich Tomi and Anthony J. Tromba, Existence theorems for minimal surfaces of nonzero genus spanning a contour, Mem. Amer. Math. Soc. 71 (1988), no. 382, iv+83. MR 920962, DOI 10.1090/memo/0382

William P. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. (N.S.) 19 (1988), no. 2, 417–431. MR 956596, DOI 10.1090/S0273-0979-1988-15685-6

[Th2]

-, Earthquakes in two dimensional hyperbolic geometry, preprint.

W. A. Veech, Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards, Invent. Math. 97 (1989), no. 3, 553–583. MR 1005006, DOI 10.1007/BF01388890

Michael Wolf, The Teichmüller theory of harmonic maps, J. Differential Geom. 29 (1989), no. 2, 449–479. MR 982185

Scott Wolpert, The Fenchel-Nielsen deformation, Ann. of Math. (2) 115 (1982), no. 3, 501–528. MR 657237, DOI 10.2307/2007011

Review Information:

Reviewer: Michael Wolf

Journal: Bull. Amer. Math. Soc. 29 (1993), 285-290
DOI: https://doi.org/10.1090/S0273-0979-1993-00421-X