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Norms on earthquake measures and Zygmund functions
Author(s):
Jun
Hu
Journal:
Proc. Amer. Math. Soc.
133
(2005),
193-202.
MSC (2000):
Primary 37E10;
Secondary 37F30
Posted:
June 23, 2004
MathSciNet review:
2085170
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Abstract:
The infinitesimal earthquake theorem gives a one-to-one correspondence between Thurston bounded earthquake measures and normalized Zygmund bounded functions. In this paper, we provide an intrinsic proof of a theorem given in an earlier paper by the author; that is, we show that the cross-ratio norm of a Zygmund bounded function is equivalent to the Thurston norm of the earthquake measure in the correspondence.
References:
-
- 1.
- F. P. Gardiner. Infinitesimal bending and twisting in one-dimensional dynamics. Trans. Amer. Math. Soc., 347 (3), 915-937, 1995. MR 95e:30024
- 2.
- F. P. Gardiner, J. Hu and N. Lakic. Earthquake curves. Contemporary Mathematics, Vol. 311, 141-195, 2002. MR 2003i:37033
- 3.
- J. Hu. Earthquake measure and cross-ratio distortion. IMS Preprint #2001/8, SUNY at Stony Brook (
 , to appear in Contemporary Mathematics). - 4.
- -, On a norm of tangent vectors to earthquake curves. Preprint, Dept. of Math. at Brooklyn College of CUNY, Jan. 2003 (to appear in Advances in Mathematics, Sinica).
- 5.
- W. P. Thurston. Earthquakes in two-dimensional hyperbolic geometry. In Low-dimensional Topology and Kleinian groups, Vol. 112, pp. 91-112. London Math. Soc. Lecture Note Ser., no. 112, 1986. MR 88m:57015
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Additional Information:
Jun
Hu
Affiliation:
Department of Mathematics, Brooklyn College, CUNY, Brooklyn, New York 11210
Email:
jun@sci.brooklyn.cuny.edu
DOI:
10.1090/S0002-9939-04-07545-8
PII:
S 0002-9939(04)07545-8
Keywords:
Earthquake measures,
Zygmund functions
Received by editor(s):
March 14, 2003
Received by editor(s) in revised form:
September 19, 2003
Posted:
June 23, 2004
Additional Notes:
This work was supported in part by an NSF postdoctoral research fellowship (DMS 9804393), an Incentive Scholar Fellowship of The City University of New York (2000-01) and PSC-CUNY research grants.
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2004,
American Mathematical Society
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