Abstract
This paper shows that, in dimensions two or more, there are no holomorphic isometries between Teichmüller spaces and bounded symmetric domains in their intrinsic Kobayashi metric.
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S. M. Antonakoudis. A note on Teichmüller spaces and convex domains. In preparation.
S. M. Antonakoudis. Royden’s theorem and birational geometry. Preprint.
Bers L.: Finite dimensional Teichmüller spaces and generalizations. Bull. Amer. Math. Soc. 5, 131–172 (1981)
Bonahon F.: The geometry of Teichmüller space via geodesic currents. Invent. math. 92, 139–162 (1988)
Earle C. J., Kra I., Krushkal S. L.: Holomorphic motions and Teichmüller spaces. Trans. Amer. Math. Soc. 343, 927–948 (1994)
Earle C. J., Markovic V.: Isometries between the spaces of L 1 holomorphic quadratic differentials on Riemann surfaces of finite type. Duke Math. J. 120, 433–440 (2003)
B. Farb and D. Margalit. A Primer on Mapping Class Groups. Princeton University Press, 2012.
A. Fathi, F. Laudenbach, and V. Poénaru. Travaux de Thurston sur les surfaces. Astérisque, vol. 66–67, 1979.
F. P. Gardiner and N. Lakic. Quasiconformal Teichmüller Theory. Amer. Math. Soc., 2000.
S. Helgason. Differential Geometry, Lie Groups, and Symmetric Spaces. Academic Press, 1978.
Hubbard J., Masur H.: Quadratic differentials and foliations. Acta Math. 142, 221–274 (1979)
J. H. Hubbard. Teichmüller Theory, vol. I. Matrix Editions, 2006.
Kerckhoff S., Masur H., Smillie J.: Ergodicity of billiard flows and quadratic differentials. Ann. of Math. 124, 293–311 (1986)
S. Kobayashi. Hyperbolic Manifolds and Holomorphic Mappings. Marcel Dekker, Inc., 1970.
S. Kobayashi. Hyperbolic Complex Spaces. Springer-Verlag, 1998.
Kubota Y.: On the Kobayashi and Carathéodory distances of bounded symmetric domains. Kodai Math. J. 12, 41– (1989)
Masur H.: Uniquely ergodic quadratic differentials. Comment. Math. Helv. 55, 255–266 (1980)
McMullen C.: Billiards and Teichmüller curves on Hilbert modular surfaces. J. Amer. Math. Soc. 16, 857–885 (2003)
C. McMullen. Entropy on Riemann surfaces and Jacobians of finite covers. Comment. Math. Helv., to appear.
Rees M.: Teichmüller distance for analytically finite surfaces is C 2. Proc. London Math. Soc. 85(3), 686–716 (2002)
Rees M.: Teichmüller distance is not \({C^{2+\epsilon}}\). Proc. London Math. Soc. (3) 88, 114–134 (2004)
H. L. Royden. Automorphisms and isometries of Teichmüller space. In Advances in the Theory of Riemann Surfaces, pages 369–384. Princeton University Press, 1971.
I. Satake. Algebraic Structures of Symmetric Domains. Princeton University Press, 1980.
Słodkowski Z.: Holomorphic motions and polynomial hulls. Proc. Amer. Math. Soc. 111, 347–355 (1991)
Tanigawa H.: Holomorphic mappings into Teichmüller spaces. Proc. Amer. Math. Soc. 117, 71–78 (1993)
Veech W.: Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards. Invent. math. 97, 553–583 (1989)
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Antonakoudis, S.M. Teichmüller spaces and bounded symmetric domains do not mix isometrically. Geom. Funct. Anal. 27, 453–465 (2017). https://doi.org/10.1007/s00039-017-0404-0
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DOI: https://doi.org/10.1007/s00039-017-0404-0