References
W. Abikoff (1977) ArticleTitleDegenerating families of Riemann surfaces Ann. Math. 105 29–44 Occurrence Handle442293 Occurrence Handle10.2307/1971024
L. Ahlfors (1961) ArticleTitleSome remarks on Teichmüller’s space of Riemann surfaces Ann. Math. 74 171–191 Occurrence Handle204641 Occurrence Handle10.2307/1970309
Al’ber (1967) ArticleTitleSpaces of mappings into a manifold with negative curvature Soviet Math. Dokl. 9 6–9 Occurrence Handle0165.55704
L. Bers (1974) Spaces of Degenerating Riemann Surfaces in Discontinous Groups and Riemann Surfaces, Ann. Math. Stud. 79 Princeton University Press Princeton, New Jersey
Brock, J. and Farb, B.: Curvature and rank of Teichmüller space, preprint 2001.
P. Buser (1992) Geometry and Spectra of Compact Riemann Surfaces Birkhäuser Boston Occurrence Handle0770.53001
T. Chu (1976) ArticleTitleThe Weil-Petersson metric in moduli space Chinese J. Math. 4 29–51 Occurrence Handle590105 Occurrence Handle0344.32006
J. Eells L. Lemaire (1981) ArticleTitleDeformations of metrics and associated harmonic mappings Proc. Indian Acad. Sci. 90 33–45 Occurrence Handle10.1007/BF02867016
J. Eells J. Sampson (1964) ArticleTitleHarmonic mappings of Riemannian manifolds Amer. J. Math. 86 109–160 Occurrence Handle164306 Occurrence Handle10.2307/2373037
D. Gilbarg N. Trudinger (1983) Elliptic Partial Differential Equations of Second Order EditionNumber2 Springer New York Occurrence Handle10.1007/978-3-642-61798-0
P. Hartman (1967) ArticleTitleOn homotopic harmonic maps Canad. J. Math. 19 673–687 Occurrence Handle214004 Occurrence Handle10.4153/CJM-1967-062-6
R. Hardt M. Wolf (1997) ArticleTitleHarmonic Extensions of quasiconformal maps to hyperbolic space Indiana Univ. Math. J. 46 155–163 Occurrence Handle1462800 Occurrence Handle10.1512/iumj.1997.46.1351
J. Jost (1990) Two Dimensional Geometric Variational Problems Wiley-Interscience New York Occurrence Handle0850.58010
J. Lohkamp (1991) ArticleTitleHarmonic diffeomorphisms and Teichmüller theory Manuscripta Math. 71 339–360 Occurrence Handle1104989 Occurrence Handle10.1007/BF02568411
H. Masur (1976) ArticleTitleThe extension of the WeilΓ–Petersson metric to the boundary of Teichmüller space Duke Math J. 43 623–635 Occurrence Handle417456 Occurrence Handle10.1215/S0012-7094-76-04350-7
D. Mumford (1977) ArticleTitleStability of projective varieties Enseign. Math. 23 39–110 Occurrence Handle450272 Occurrence Handle0363.14003
S. Nag (1988) Complex Analytic Theory of Teichmüuller Wiley New York Occurrence Handle0667.30040
H. Omori (1967) ArticleTitleIsometric immersions of Riemannian manifolds J. Math. Soc. Japan 19 205–241 Occurrence Handle215259 Occurrence Handle10.2969/jmsj/01920205
H. Royden (1974) ArticleTitleIntrinsic metrics on Teichmüller space Proc. Int. Congr. Math. 2 217–221 Occurrence Handle0298.32014
J. Sampson (1978) ArticleTitleSome properties and applications of harmonic mappings Ann. Sci. Ecole Norm. Sup. 4 211–228 Occurrence Handle510549 Occurrence Handle10.24033/asens.1344
G. Schumacher (1986) ArticleTitleHarmonic maps of the moduli space of compact Riemann surfaces Math. Ann. 275 455–466 Occurrence Handle858289 Occurrence Handle10.1007/BF01458616
R. Schoen S. Yau (1976) ArticleTitleHarmonic maps and the topology of stable hypersurfaces and manifolds of non-negative Ricci curvature Comment Math. Helv. 51 333–341 Occurrence Handle438388 Occurrence Handle10.1007/BF02568161
A. Tromba (1987) ArticleTitleOn an energy function for the WeilΓ–Petersson metric on Teichmüller space Manuscripta Math. 59 249–260 Occurrence Handle905201 Occurrence Handle10.1007/BF01158050
A. Tromba (1992) Teichmüller Theory in Riemannian Geometry Birkhauser Basel Occurrence Handle10.1007/978-3-0348-8613-0
M. Wolf (1989) ArticleTitleTeichmüller theory of harmonic maps J. Differential Geom. 29 449–479 Occurrence Handle982185 Occurrence Handle10.4310/jdg/1214442885
M. Wolf (1991) ArticleTitleInfinite energy harmonic maps and degeneration on hyperbolic surfaces in moduli space J. Differential Geom. 33 487–539 Occurrence Handle1094467 Occurrence Handle10.4310/jdg/1214446328
M. Wolf S. Wolpert (1992) ArticleTitleReal analytic structures on the moduli space of curves Amer. J. Math. 114 1079–1102 Occurrence Handle1183532 Occurrence Handle10.2307/2374890
S. Wolpert (1975) ArticleTitleNoncompleteness of the Weil-Petersson metric for Teichmüller space Pacific J. Math. 61 573–577 Occurrence Handle422692 Occurrence Handle10.2140/pjm.1975.61.573
S. Wolpert (1986) ArticleTitleChern forms and the Riemann tensor for the moduli space of curves Invent. Math. 85 119–145 Occurrence Handle842050 Occurrence Handle10.1007/BF01388794
Wolpert, S.: Geometry of the Weil-Petersson completion of Teichmüller space, preprint 2002
S.-T. Yau (1986) ArticleTitleHarmonic functions on complete Riemannian manifolds Comm. Pure Appl. Math. 28 119–145 Occurrence Handle431040
Author information
Authors and Affiliations
Corresponding author
Additional information
Mathematics Subject Classifications (2000). 32G15, 53C21, 30F60.
Rights and permissions
About this article
Cite this article
Huang, Z. Asymptotic Flatness of the Weil-Petersson Metric on Teichmüller Space. Geom Dedicata 110, 81–102 (2005). https://doi.org/10.1007/s10711-003-0816-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10711-003-0816-x