Norms on earthquake measures and Zygmund functions

Author:
Jun Hu

Journal:
Proc. Amer. Math. Soc. **133** (2005), 193-202

MSC (2000):
Primary 37E10; Secondary 37F30

Published electronically:
June 23, 2004

MathSciNet review:
2085170

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Abstract | References | Similar Articles | Additional Information

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.

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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:
http://dx.doi.org/10.1090/S0002-9939-04-07545-8

Keywords:
Earthquake measures,
Zygmund functions

Received by editor(s):
March 14, 2003

Received by editor(s) in revised form:
September 19, 2003

Published electronically:
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

Article copyright:
© Copyright 2004
American Mathematical Society